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The value of int0^oo(x dx)/((1+x)(1+x^2)...

The value of `int_0^oo(x dx)/((1+x)(1+x^2))` is equal to

A

`(pi)/4`

B

`(pi)/2`

C

`pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Put` x=tan theta` and `dx=sec^(2) theta d theta`
`:. I=int_(0)^(pi//2)(tan theta sec^(2) theta)/((1+tan theta)(sec^(2)theta)) d theta` …………1
`:. I=int_(0)^(pi//2)(sin theta d theta)/(cos theta +sin theta)=(pi)/4`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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