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int0^oo(dx)/([x+sqrt(x^2+1)]^3)i se q u ...

`int_0^oo(dx)/([x+sqrt(x^2+1)]^3)i se q u a lto` `3/8` (b) `1/8` (c) `-3/8` (d) none of these

A

`3/8`

B

`1/8`

C

`-3/8`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Putting `x=tan theta` we get ,
`int_(0)^(pi//2) (dx)/([x+sqrt(x^(2)+1]^(3)))=int_(0)^(pi/2) (sec^(2) theta d theta)/((tan theta +sec theta)^(3))`
`=int_(0)^(pi//2) (cos theta)/((1+sin theta)^(3))d theta`
`=[-1/(2(1+sin theta)^(2))]_(0)^(pi//2)=-1/8+1/2=3/8`
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