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The value of the integral underset(-1)...

The value of the integral
`underset(-1)overset(3 )int ("tan"^(1)(x)/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/(x))dx` is equal to

A

`pi`

B

`2pi`

C

`4pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`underset(-1)overset(3)int ("tan"^(1)(x)/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/(x))dx`
`=underset(-1)overset(3)int ("tan"^(1)(x)/(x^(2)+1)+"cot"^(-1)(x^(2)+1)/(x))dunderset(-1)overset(3)int(pi)/(2)dx=2pi`
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