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inte^(tan^(-1)x)(1+(x)/(1+x^(2)))dx is e...

`inte^(tan^(-1)x)(1+(x)/(1+x^(2)))dx` is equal to

A

`xe^(tan^(-1)x)+C`

B

`x^(2)e^(tan^(-1)x)+C`

C

`(1)/(x)e^(tan^(-1)x)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Put `tan^(-1)x=t rArr (dx)/(1+x^(2))=dt`
`therefore int e^(tan^(-1)x)((1+x+x^(2))/(1+x^(2)))dx=inte^(y)(tan t+sec^(2)t)dt`
`" "=e^(t) tan t +C = xe^(tan^(-1))+C`
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