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sin^(-1) ((2x)/(1 + x^(2)))...

`sin^(-1) ((2x)/(1 + x^(2)))`

A

`x tan^(-1)x-In|sec(tan^(-1)x)|+c`

B

`x tan^(-1)x+In|sec(tan^(-1)x)|+c`

C

`x tan^(-1)x-In|cos(tan^(-1)x)|+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`I= int sin^(-1)((2x)/(1+x^(2)))dx`
`"Let " x=tan theta`
`"or " dx=sec^(2)theta d theta `
` :. I=intsin^(-1)((2tan theta)/(1+tan^(2)theta))sec^(2) theta d theta `
` =2 int theta sec^(2)thetad theta `
`=2(theta tan theta-In|sec theta|)+C`
`=2(xtan^(-1)x-In|sec(tan^(-1)x)|)+C`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
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  2. Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is varp...

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  3. sin^(-1) ((2x)/(1 + x^(2)))

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  4. If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x...

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  5. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

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  6. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  7. "If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

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  8. int x sinx sec^(3)x dx is equal to

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  9. int e^(tan^-1x)(1+x+x^2) d(cot^-1x) is equal to

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  10. int e^(x)((2 tanx)/(1+tanx)+cot^(2)(x+(pi)/(4)))dx is equal to

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  11. inte^x^4(x+x^3+2x^5)e^x^2dxis equal to 1/2x e^x^2e^x^4+c (b) 1/2x^2e...

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  12. The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)...

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  13. int e^(x)((x^(2)+1))/((x+1)^(2))dx is equal to

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  14. int ((x+2)/(x+4))^2 e^x dx is equal to

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  15. inte^(tanx)(sinx-secx)dx is equal to

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  16. int(cosec^2x-2005)/cos^[2005]x.dx

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  17. int(1+x-(1)/(x))e^(x+(1)/(x)) dx is equal to

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  18. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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  19. Ifxf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x))^...

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  20. The value of int((ax^2-b)dx)/(xsqrt(c^2x^2-(ax^2+b)^2)) is equal to

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