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int(1)^(0)((tan^(-1)x)/x + (lnx)/(1+x^(2...

`int_(1)^(0)((tan^(-1)x)/x + (lnx)/(1+x^(2)))` dx is equal to

A

`1/e_(tan^(-1)e)`

B

`tan^(-1)e`

C

`etan^(-1) (1/e)`

D

`tan^(-1)(lne)`

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(1)^(e)tan^(-1)x. 1/x dx + int_(1)^(e)(ln x)/(1+x^(2)) dx`
`=(tan^(-1) x ln x)_(1)^(e) - int_(1)^(e) 1/(1+x^(2)) ln dx + int_(1)^(e) (ln x)/(1+x^(2)) dx`
`=tan^(-1)(e). Lne - tan^(-1)(1).ln1`
`= tan^(-1)(e)`
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