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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: FORMULAE......plzzz dont neglect......!!!!!
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[Post New]16 Aug 2007 14:10:08 IST
    Subject: FORMULAE......plzzz dont neglect......!!!!!
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nivedh_89 (4512)

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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_89 (4512)

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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...!!!
 this reply: 45 points  (with 9 Olaaa!! Perrrfect answer.   in 9 votes )   [?]
 
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[Post New]16 Aug 2007 14:11:26 IST
    Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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nivedh_89 (4512)

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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...!!!
 this reply: 52 points  (with 10 Olaaa!! Perrrfect answer.   in 11 votes )   [?]
 
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[Post New]16 Aug 2007 14:12:07 IST
    Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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nivedh_89 (4512)

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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...!!!
 this reply: 25 points  (with 5 Olaaa!! Perrrfect answer.   in 5 votes )   [?]
 
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[Post New]16 Aug 2007 14:12:43 IST
    Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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nivedh_89 (4512)

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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: 20 points  (with 4 Olaaa!! Perrrfect answer.   in 4 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_89 (4512)

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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...!!!
 this reply: 15 points  (with 3 Olaaa!! Perrrfect answer.   in 3 votes )   [?]
 
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[Post New]16 Aug 2007 14:16:08 IST
    Subject: Re:FORMULAE......plzzz dont neglect......!!!!!
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nivedh_89 (4512)

Blazing goIITian

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

1.