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Ask community Community Discussion Question: FORMULAE......plzzz dont neglect......!!!!!
Reply Forum Index -> Integral Calculus originally posted here on IIT-JEE / AIEEE community   
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[Post New] 16 Aug 2007 14:10:08 IST
   Subject: FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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Hi guys n gals here r some more of those integration formulae..........!!!!!!!
I HOPE IT PROVES USEFUL TO ALL OF U.............!!!!!!!!!!!!!!!
it contains many formulae....do refer it............it CONTAINS ALL THOSE FORMULAE WITH WCH INTEGRATION QUESTIONS IN IIT R BASED ON.......
..............................!!!!!!!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
    
[Post New] 16 Aug 2007 14:10:30 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING x2+a2

1.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle2}+a^{displaystyle2}}=displaystyle rac{1}{a} an^{displaystyle-1}displaystyle rac{x}{a}$
2.
$displaystyle intdisplaystyle rac{x,dx}{x^{displaystyle2}+a^{displaystyle2}}=displaystyle rac{1}{2}ln(x^{displaystyle2}+a^{displaystyle2})$
3.
$displaystyle intdisplaystyle rac{x^{displaystyle2},dx}{x^{displaystyle2}+a^{displaystyle2}}=x-a an^{displaystyle-1}displaystyle rac{x}{a}$
4.
$displaystyle intdisplaystyle rac{x^{displaystyle3},dx}{x^{displaystyle2... ...laystyle rac{a^{displaystyle2}}{2}ln(x^{displaystyle2}+a^{displaystyle2})$
5.
$displaystyle intdisplaystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
6.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle2}(x^{displaystyle2}... ...yle rac{1}{a^{displaystyle3}} an^{displaystyle-1}displaystyle rac{x}{a}$
7.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle3}(x^{displaystyle2}... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
8.
$displaystyle intdisplaystyle rac{dx}{(x^{displaystyle2}+a^{displaystyle2... ...le rac{1}{2a^{displaystyle3}} an^{displaystyle-1}displaystyle rac{x}{a}$
9.
$displaystyle intdisplaystyle rac{x,dx}{(x^{displaystyle2}+a^{displaysty... ...splaystyle2}}=displaystyle rac{-1}{2(x^{displaystyle2}+a^{displaystyle2})}$
10.
$displaystyle intdisplaystyle rac{x^{displaystyle2},dx}{(x^{displaystyle... ...e2})}+displaystyle rac{1}{2a} an^{displaystyle-1}displaystyle rac{x}{a}$
11.
$displaystyle intdisplaystyle rac{x^{displaystyle3},dx}{(x^{displaystyle... ...aystyle2})}+displaystyle rac{1}{2}ln(x^{displaystyle2}+a^{displaystyle2})$
12.
$displaystyle intdisplaystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
13.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle2}(x^{displaystyle2}... ...le rac{3}{2a^{displaystyle5}} an^{displaystyle-1}displaystyle rac{x}{a}$
14.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle3}(x^{displaystyle2}... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
15.
$displaystyle intdisplaystyle rac{dx}{(x^{displaystyle2}+a^{displaystyle2... ...laystyle rac{dx}{(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n-1}}$
16.
$displaystyle intdisplaystyle rac{x,dx}{(x^{displaystyle2}+a^{displaysty... ...le rac{-1}{2(n-1)(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n-1}}$
17.
$displaystyle intdisplaystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle... ...aystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n-1}}$
18.
$displaystyle intdisplaystyle rac{x^{displaystyle m},dx}{(x^{displaystyl... ...splaystyle m-2},dx}{(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n}}$
19.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle m}(x^{displaystyle2... ...x^{displaystyle m-2}(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n}}$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:11:26 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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Common Integrals INTEGRALS CONTAINING ax+b

1.
$displaystyle intdisplaystyle rac{dx}{ax+b}=displaystyle rac{1}{a}ln(ax+b)$
2.
$displaystyle intdisplaystyle rac{x,dx}{ax+b}=displaystyle rac{x}{a}-displaystyle rac{b}{a^{2}}ln(ax+b)$
3.
$displaystyle intdisplaystyle rac{x^3,dx}{ax+b}=displaystyle rac{(ax+b)... ...splaystyle rac{3b^{2}(ax+b)}{a^{4}}- displaystyle rac{b^{3}}{a^4}ln(ax+b)$
4.
$displaystyle intdisplaystyle rac{x^2,dx}{ax+b}=displaystyle rac{(ax+b)... ...displaystyle rac{2b(ax+b)}{a^{3}}+displaystyle rac{b^{2}}{a^{3}}ln(ax+b)$
5.
$displaystyle intdisplaystyle rac{dx}{x(ax+b)}=displaystyle rac{1}{b}lnleft(displaystyle rac{x}{ax+b} ight)$
6.
$displaystyle intdisplaystyle rac{dx}{x^{2}(ax+b)}=-displaystyle rac{1}{bx}+displaystyle rac{a}{b^{2}}lnleft(displaystyle rac{ax+b}{x} ight)$
7.
$displaystyle intdisplaystyle rac{dx}{x^{3}(ax+b)}=displaystyle rac{2ax-... ...}+displaystyle rac{a^{2}}{b^{3}}lnleft(displaystyle rac{x}{ax+b} ight)$
8.
$displaystyle intdisplaystyle rac{dx}{(ax+b)^{2}}=displaystyle rac{-1}{a(ax+b)}$
9.
$displaystyle intdisplaystyle rac{x,dx}{(ax+b)^{2}}=displaystyle rac{b}{a^{2}(ax+b)}+displaystyle rac{1}{a^{2}}ln(ax+b)$
10.
$displaystyle intdisplaystyle rac{x^{2},dx}{(ax+b)^{2}}=displaystyle ra... ...displaystyle rac{b^{2}}{a^{3}(ax+b)}-displaystyle rac{2b}{a^{3}}ln(ax+b)$
11.
$displaystyle intdisplaystyle rac{x^{3},dx}{(ax+b)^{2}}=displaystyle ra... ...playstyle rac{b^{3}}{a^{4}(ax+b)}+displaystyle rac{3b^{2}}{a^{4}}ln(ax+b)$
12.
$displaystyle intdisplaystyle rac{dx}{x(ax+b)}=displaystyle rac{1}{b(ax+b)}+displaystyle rac{1}{b^{2}}lnleft(displaystyle rac{x}{ax+b} ight)$
13.
$displaystyle intdisplaystyle rac{dx}{x^{2}(ax+b)^{2}}=displaystyle rac{... ...2}x}+displaystyle rac{2a}{b^{3}}lnleft(displaystyle rac{ax+b}{x} ight)$
14.
$displaystyle intdisplaystyle rac{dx}{x^{3}(ax+b)^{2}}=-displaystyle rac... ...-displaystyle rac{3a^{2}}{b^{4}}lnleft(displaystyle rac{ax+b}{x} ight)$
15.
$displaystyle intdisplaystyle rac{dx}{(ax+b)^{3}}=displaystyle rac{-1}{2(ax+b)^{2}}$
16.
$displaystyle intdisplaystyle rac{x,dx}{(ax+b)^{3}}=displaystyle rac{-1}{a^{2}(ax+b)}+displaystyle rac{b}{2a^{2}(ax+b)^{2}}$
17.
$displaystyle intdisplaystyle rac{x^{2},dx}{(ax+b)^{3}}=displaystyle ra... ...playstyle rac{b^{2}}{2a^{3}(ax+b)^{2}}+displaystyle rac{1}{a^{3}}ln(ax+b)$
18.
$displaystyle intdisplaystyle rac{x^{3},dx}{(ax+b)^{3}}=displaystyle ra... ...splaystyle rac{b^3}{2a^{4}(ax+b)^{2}}-displaystyle rac{3b}{a^{4}}ln(ax+b)$
19.
$displaystyle intdisplaystyle rac{dx}{x(ax+b)^{3}}=displaystyle rac{a^{2... ...x+b)}-displaystyle rac{1}{b^{3}}lnleft(displaystyle rac{ax+b}{x} ight)$
20.
$displaystyle intdisplaystyle rac{dx}{x^{2}(ax+b)^{3}}=displaystyle rac{... ...3}x}+displaystyle rac{3a}{b^{4}}lnleft(displaystyle rac{ax+b}{x} ight)$
21.
$displaystyle intdisplaystyle rac{dx}{x^{3}(ax+b)^{3}}=displaystyle rac{... ...-displaystyle rac{6a^{2}}{b^{5}}lnleft(displaystyle rac{ax+b}{x} ight)$
22.
$displaystyle int(ax+b)^{displaystyle n},dx=displaystyle rac{(ax+b)^{displaystyle n+1}}{(n+1)a}, ,;; n eq -1$
23.
$displaystyle int x(ax+b)^{displaystyle n},dx = displaystyle rac{(ax+b)^{... ...e rac{b(ax+b)^{displaystyle n+1}}{(n+1)a^{displaystyle2}},;;;n eq -1,-2$
24.
$displaystyle int x^{displaystyle2}(ax+b)^{displaystyle n},dx=displaystyle... ...ystyle2}(ax+b)^{displaystyle n+1}}{(n+1)a^{displaystyle3}};,;n eq -1,-2,-3$
25.
$displaystyle int x^{displaystyle m}(ax+b)^{displaystyle n},dx=left{ eg... ... int x^{displaystyle m}(ax+b)^{displaystyle{n+1}},dx end{array} ight. $
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:12:07 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b

1.
$displaystyle intdisplaystyle rac{dx}{displaystyle sqrt{ax+b}}=displaystyle rac{2displaystyle sqrt{ax+b}}{a}$
2.
$displaystyle intdisplaystyle rac{x,dx}{displaystyle sqrt{ax+b}}=displaystyle rac{2(ax-2b)}{3a^{displaystyle2}}displaystyle sqrt{ax+b}$
3.
$displaystyle intdisplaystyle rac{x^{displaystyle2},dx}{displaystyle sq... ...le2}-4abx+8b^{displaystyle 2})}{15a^{displaystyle3}}displaystyle sqrt{ax+b}$
4.
$displaystyle intdisplaystyle rac{dx}{xdisplaystyle sqrt{ax+b}}=left{ ... ...tyle-1}displaystyle sqrt{displaystyle rac{ax+b}{-b}} end{array} ight. $
5.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle 2}displaystyle sqr... ...rac{a}{2b}displaystyle intdisplaystyle rac{dx}{xdisplaystyle sqrt{ax+b}}$
6.
$displaystyle intdisplaystyle sqrt{ax+b},dx=displaystyle rac{2displaystyle sqrt{(ax+b)^{displaystyle3}}}{3a}$
7.
$displaystyle int xdisplaystyle sqrt{ax+b},dx=displaystyle rac{2(3ax-2b)}{15a^{displaystyle2}}displaystyle sqrt{(ax+b)^{displaystyle3}}$
8.
$displaystyle int x^{displaystyle2}displaystyle sqrt{ax+b},dx=displaystyl... ...aystyle 2})}{105a^{displaystyle3}}displaystyle sqrt{(a+bx)^{displaystyle3}}$
9.
$displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x},dx=2displ... ...rt{ax+b}+bdisplaystyle intdisplaystyle rac{dx}{xdisplaystyle sqrt{ax+b}}$
10.
$displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaysty... ...frac{a}{2}displaystyle intdisplaystyle rac{dx}{xdisplaystyle sqrt{ax+b}}$
11.
$displaystyle intdisplaystyle rac{x^{displaystyle m}}{displaystyle sqrt{... ...e intdisplaystyle rac{x^{displaystyle m-1}}{displaystyle sqrt{ax+b}},dx$
12.
$displaystyle intdisplaystyle rac{dx}{x^{displaystyle m}displaystyle sqr... ...yle intdisplaystyle rac{dx}{x^{displaystyle m-1}displaystyle sqrt{ax+b}}$
13.
$displaystyle int x^{displaystyle m}displaystyle sqrt{ax+b},dx=displaysty... ...}{(2m+3)a}displaystyle int x^{displaystyle m-1}displaystyle sqrt{ax+b},dx$
14.
$displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaysty... ...yle intdisplaystyle rac{dx}{x^{displaystyle m-1}displaystyle sqrt{ax+b}}$
15.
$displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaysty... ...e intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaystyle m-1}},dx$
16.
$displaystyle int(ax+b)^{displaystyle m/2},dx=displaystyle rac{2(ax+b)^{displaystyle(m+2)/2}}{a(m+2)}$
17.
$displaystyle int x(ax+b)^{displaystyle m/2},dx=displaystyle rac{2(ax+b)^... ...}-displaystyle rac{2b(ax+b)^{displaystyle(m+2)/2}}{a^{displaystyle2}(m+2)}$
18.
$egin{array}{lcl} displaystyle int x^{displaystyle2}(ax+b)^{displaystyle m... ...splaystyle2}(ax+b)^{displaystyle(m+2)/2}}{a^{displaystyle3}(m+2)} end{array}$
19.
$displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m/2}}{x},dx=displ... ...m}+bdisplaystyle intdisplaystyle rac{(ax+b)^{displaystyle(m-2)/2}}{x},dx$
20.
$displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m/2}}{x^{displayst... ...ma}{2b}displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m/2}}{x},dx$
21.
$displaystyle intdisplaystyle rac{dx}{x(ax+b)^{displaystyle m/2}}=display... ...{1}{b}displaystyle intdisplaystyle rac{dx}{x(ax+b)^{displaystyle(m-2)/2}}$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:12:43 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING ax+b AND px+q


1.
$displaystyle intdisplaystyle rac{dx}{(ax+b)(px+q)}=displaystyle rac{1}{bp-aq}lnleft(displaystyle rac{px+q}{ax+b} ight)$
2.
$displaystyle intdisplaystyle rac{x,dx}{(ax+b)(px+q)}=displaystyle rac{... ...{displaystyle rac{b}{a}ln(ax+b)-displaystyle rac{q}{p}ln(px+q) ight}$
3.
$displaystyle intdisplaystyle rac{dx}{(ax+b)^{displaystyle 2}(px+q)}=disp... ...laystyle rac{p}{bp-aq}lnleft(displaystyle rac{px+q}{ax+b} ight) ight}$
4.
$displaystyle intdisplaystyle rac{x,dx}{(ax+b)^{displaystyle2}(px+q)}=di... ...(displaystyle rac{ax+b}{px+q} ight)-displaystyle rac{b}{a(ax+b)} ight}$
5.
$displaystyleegin{array}{l} displaystyle intdisplaystyle rac{x^{display... ...displaystyle rac{b(bp-2aq)}{a^{displaystyle2}}ln(ax+b) ight} end{array}$
6.
$displaystyleegin{array}{l} displaystyle intdisplaystyle rac{dx}{(ax+b)^... ...rac{dx}{(ax+b)^{displaystyle m}(px+q)^{displaystyle n-1}} ight} end{array}$
7.
$displaystyle intdisplaystyle rac{ax+b}{px+q},dx=displaystyle rac{ax}{p}+displaystyle rac{bp-aq}{p^{displaystyle2}}ln(px+q)$
8.
$displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m}}{(px+q)^{displa... ...displaystyle m-1}}{(px+q)^{displaystyle n-1}},dx ight} end{array} ight.$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
  this reply:   25 points  (with 5  Olaaa!! Perrrfect answer.   in 5   votes   )     [?]
 
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[Post New] 16 Aug 2007 14:13:23 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b AND px+q

1.
$displaystyle intdisplaystyle rac{px+q}{displaystyle sqrt{ax+b}},dx=displaystyle rac{2(apx+3aq-2bp)}{3a^{displaystyle2 }}displaystyle sqrt{ax+b}$
2.
$displaystyle intdisplaystyle rac{dx}{(px+q)displaystyle sqrt{ax+b}}=lef... ...1}displaystyle sqrt{displaystyle rac{p(ax+b)}{aq-bp}} end{array} ight.$
3.
$displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{px+q},dx=lef... ...1}displaystyle sqrt{displaystyle rac{p(ax+b)}{aq-bp}} end{array} ight.$
4.
$displaystyle int(px+q)^{displaystyle n}displaystyle sqrt{ax+b},dx=displa... ...intdisplaystyle rac{(px+q)^{displaystyle n}}{displaystyle sqrt{ax+b}},dx$
5.
$displaystyle intdisplaystyle rac{(px+q)^{displaystyle n}}{displaystyle ... ...tdisplaystyle rac{(px+q)^{displaystyle n-1},dx}{displaystyle sqrt{ax+b}}$
6.
$displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{(px+q)^{displ... ...intdisplaystyle rac{dx}{(px+q)^{displaystyle n-1}displaystyle sqrt{ax+b}}$
7.
$displaystyle egin{array}{l} displaystyle intdisplaystyle rac{dx}{(px+q... ...frac{dx}{(px+q)^{displaystyle n-1}displaystyle sqrt{ax+b}} ight.end{array}$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:16:08 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING THE SQUARE ROOTS OF BOTH ax+b AND px+q

1.
$\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}=\l... ...displaystyle \sqrt{\displaystyle \frac{-p(ax+b)}{a(px+q)}} \end{array} \right.$
2.
$\displaystyle \int\displaystyle \frac{x\,dx}{\displaystyle \sqrt{(ax+b)(px+q)}}... ...ap}\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}$
3.
$\begin{array}{lcl} \displaystyle \int\displaystyle \sqrt{(ax+b)(px+q)}\,dx&=&\d... ...style \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}\end{array}$
4.
$\displaystyle \int\displaystyle \sqrt{\displaystyle \frac{px+q}{ax+b}}\,dx=\dis... ...2a}\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}$
5.
$\displaystyle \int\displaystyle \frac{dx}{(px+q)\displaystyle \sqrt{(ax+b)(px+q... ...isplaystyle \frac{2\displaystyle \sqrt{ax+b}}{(aq-bp)\displaystyle \sqrt{px+q}}$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:37:46 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING x2-a2

We assume x2 > a2:
1.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}-a^{\displaystyle2}}=\displaystyle \frac{1}{2a}\ln\left(\displaystyle \frac{x-a}{x+a}\right)\;\;$ or $\;\;-\displaystyle \frac{1}{a}$coth $^{\displaystyle-1}\displaystyle \frac{x}{a}$
2.
$\displaystyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle2}-a^{\displaystyle2}}=\displaystyle \frac{1}{2}\ln(x^{\displaystyle2}-a^{\displaystyle2})$
3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{x^{\displaystyle2... ...yle2}}=x+\displaystyle \frac{a}{2}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
4.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{x^{\displaystyle2... ...laystyle \frac{a^{\displaystyle2}}{2}\ln(x^{\displaystyle2}-a^{\displaystyle2})$
5.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle... ...aystyle \frac{x^{\displaystyle2}-a^{\displaystyle2}}{x^{\displaystyle2}}\right)$
6.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle2}... ...tyle \frac{1}{2a^{\displaystyle3}}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
7.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}(x^{\displaystyle2}... ...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}-a^{\displaystyle2}}\right)$
8.
$\displaystyle \int\displaystyle \frac{dx}{(x^{\displaystyle2}-a^{\displaystyle2... ...tyle \frac{1}{4a^{\displaystyle3}}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
9.
$\displaystyle \int\displaystyle \frac{x\,dx}{(x^{\displaystyle2}-a^{\displaysty... ...splaystyle2}}=\displaystyle \frac{-1}{2(x^{\displaystyle2}-a^{\displaystyle2})}$
10.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(x^{\displaystyle... ...yle2})}+\displaystyle \frac{1}{4a}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
11.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{(x^{\displaystyle... ...aystyle2})}+\displaystyle \frac{1}{2}\ln(x^{\displaystyle2}-a^{\displaystyle2})$
12.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle... ...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}-a^{\displaystyle2}}\right)$
13.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle2}... ...tyle \frac{3}{4a^{\displaystyle5}}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
14.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}(x^{\displaystyle2}... ...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}-a^{\displaystyle2}}\right)$
15.
$\displaystyle \int\displaystyle \frac{dx}{(x^{\displaystyle2}-a^{\displaystyle2... ...laystyle \frac{dx}{(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
16.
$\displaystyle \int\displaystyle \frac{x\,dx}{(x^{\displaystyle2}-a^{\displaysty... ...le \frac{-1}{2(n-1)(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
17.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle... ...aystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
18.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{(x^{\displaystyl... ...splaystyle m-2}\,dx}{(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n}}$
19.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}(x^{\displaystyle2... ...x^{\displaystyle m}(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:39:24 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING ax2+bx+c


1.
$\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}=\left\{\beg... ...{2ax+b+\displaystyle \sqrt{b^{\displaystyle2}-4ac}}\right) \end{array} \right.$
2.
$\displaystyle \int\displaystyle \frac{x\,dx}{ax^{\displaystyle2}+bx+c}=\display... ...\frac{b}{2a}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{ax^{\displaystyle... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
4.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}}{ax^{\displaystyle2}+... ...le \int\displaystyle \frac{x^{\displaystyle m-1}\,dx}{ax^{\displaystyle2}+bx+c}$
5.
$\displaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)}=\display... ...\frac{b}{2c}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
6.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(ax^{\displaystyle2... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
7.
$\begin{array}{ll} \displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle n}... ...laystyle \frac{dx}{x^{\displaystyle n-2}(ax^{\displaystyle2}+bx+c)} \end{array}$
8.
$\displaystyle \int\displaystyle \frac{dx}{(ax^{\displaystyle2}+bx+c)^{\displays... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
9.
$\displaystyle \int\displaystyle \frac{x\,dx}{(ax^{\displaystyle2}+bx+c)^{\displ... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
10.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(ax^{\displaystyl... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$
11.
$\begin{array}{ll} \displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx... ...isplaystyle m-2}\,dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle n}} \end{array}$
12.
$\begin{array}{ll} \displaystyle \int\displaystyle \frac{x^{\displaystyle2n-1}\,... ...isplaystyle2n-2}\,dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle n}} \end{array}$
13.
$\begin{array}{ll} \displaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyle... ...splaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)} \end{array}$
14.
$\begin{array}{ll} \displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(... ...isplaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)^{\displaystyle2}} \end{array}$
15.
$\begin{array}{lcl} \displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m... ...{x^{\displaystyle m-1}(ax^{\displaystyle2}+bx+c)^{\displaystyle n}} \end{array}$
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 14:57:02 IST
   Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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Nivedh Iyer (3456)

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INTEGRALS CONTAINING "xn+an" or "xn-an"


1.
$\displaystyle \int\displaystyle \frac{dx}{x\left(x^{\displaystyle n}+a^{\displa... ...isplaystyle \frac{x^{\displaystyle n}}{x^{\displaystyle n}+a^{\displaystyle n}}$
2.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle n-1}\,dx}{x^{\displaysty... ...displaystyle \frac{1}{n}\ln\left(x^{\displaystyle n}+a^{\displaystyle n}\right)$
3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{\left(x^{\displa... ...n}\,dx}{\left(x^{\displaystyle n}+a^{\displaystyle n}\right)^{\displaystyle r}}$
4.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}\left(x^{\displays... ...yle m-n}\left(x^{\displaystyle n}+a^{\displaystyle n}\right)^{\displaystyle r}}$
5.
$\displaystyle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{x^{\displaystyle... ...ystyle n}+a^{\displaystyle n}}+\displaystyle \sqrt{a^{\displaystyle n}}}\right)$
6.
$\displaystyle \int\displaystyle \frac{dx}{x\left(x^{\displaystyle n}-a^{\displa... ...tyle \frac{x^{\displaystyle n}-a^{\displaystyle n}}{x^{\displaystyle n}}\right)$
7.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle n-1}\,dx}{x^{\displaysty... ...displaystyle \frac{1}{n}\ln\left(x^{\displaystyle n}-a^{\displaystyle n}\right)$
8.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{\left(x^{\displa... ...\,dx}{\left(x^{\displaystyle n}-a^{\displaystyle n}\right)^{\displaystyle r-1}}$
9.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}\left(x^{\displays... ...yle m}\left(x^{\displaystyle n}-a^{\displaystyle n}\right)^{\displaystyle r-1}}$
10.
$\displaystyle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{x^{\displaystyle... ...splaystyle \sqrt{\displaystyle \frac{a^{\displaystyle n}}{x^{\displaystyle n}}}$
11.
$\displaystyle \begin{array}{lcl} \displaystyle \int\displaystyle \frac{x^{\disp... ...\cos\displaystyle \frac{(2k-1)\pi}{2m}+a^{\displaystyle2}\right)\\ \end{array}$
where $0<p\leq 2m$.
12.
$\displaystyle \begin{array}{lcl} \displaystyle \int\displaystyle \frac{x^{\disp... ...^{\displaystyle2m-p}}\{\ln(x-a)+(-1)^{\displaystyle p}\ln(x+a)\}\\ \end{array}$
where $0<p\leq 2m$.
13.
$\displaystyle \begin{array}{ll} \displaystyle \int\displaystyle \frac{x^{\displ... ...(-1)^{\displaystyle p-1}\ln(x+a)}{(2m+1)a^{\displaystyle2m-p+1}}\\ \end{array}$
where $0<p\leq2m+1$.
14.
$\displaystyle\begin{array}{ll} \displaystyle \int\displaystyle \frac{x^{\displa... ...} }+\displaystyle \frac{\ln(x-a)}{(2m+1)a^{\displaystyle2m-p+1}}\\ \end{array}$
where $0<p\leq2m+1$.
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 15:09:45 IST
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plzzz do comment................!!!!!!!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 15:19:54 IST
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............................
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 16:28:17 IST
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did u all like it.................????????
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 17:20:01 IST
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Nivedh Iyer (3456)

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plzzz comment ...........!!!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 19:36:08 IST
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samvedna kaloty (91)

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hey nivedh such a post n anybody who  ll go widout likin it is gonna be greatly... unfair buddy... wonderful keep goin
best of luck..... i1 rate frm my side
brilliant brains may be found at d backbenches or even out of d class
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[Post New] 16 Aug 2007 22:25:34 IST
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thanx.................!!!!!!!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 16 Aug 2007 22:37:01 IST
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vaibhav dixit (0)

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hay nivedh telllllllllll me how one can learn such a huge list of formula?????????
 
anyways GREAT EFFORTS!!!!!!!!!!!!!!!
 
BUT stiiiiiillllll
 
 HOW????????????????
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[Post New] 16 Aug 2007 22:55:27 IST
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learn those wch u think is useful................acc 2 me u shld learn everything........!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 17 Aug 2007 14:23:05 IST
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thanx..........!!!!!!!!!!!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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[Post New] 22 Aug 2007 12:28:51 IST
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Nivedh Iyer (3456)

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some more commentzz plzzzzzzzzz...........!!!!!!!!!!!!!!!!!!
The inevitable truth of life.....everyone in our life is going 2 hurt sooner or later......u just have 2 realise who is worth.....

the PAIN or the PERSON...!!!
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