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For x >1,int sin^(- 1)((2x)/(1+x^2))dx i...

For `x >1,int sin^(- 1)((2x)/(1+x^2))dx` is equal to

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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