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If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2...

If `f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0` then the value of f(1) is

A

`e((pi)/(4)-(1)/(2))+1`

B

`e((pi)/(4)+(1)/(2))+1`

C

`e((pi)/(2)-(1)/(4))+1`

D

`e^(-1)((pi)/(4)-(1)/(2))+1`

Text Solution

Verified by Experts

The correct Answer is:
A
If `inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx`
`=inte^(x)(tan^(-1)x-(1)/(1+x^(2))+(1)/(1+x^(2))+(2x)/((1+x^(2))^(2)))dx`
`=e^(x)(tan^(-1)x-(1)/(1+x^(2)))+c`
`f(0)=0rArr c=1`
`rArr" "f(1)=e((pi)/(4)-(1)/(2))+1`
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