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The value of int1^e((tan^(-1)x)/x+(logx)...

The value of `int_1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is` (a) `tane` (b) `tan^(-1)e` (c)`tan^(-1)(1/e)` (d) none of these

A

`tane`

B

`tan^(-1)e`

C

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

D

none of these

Text Solution

Verified by Experts

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