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The integral int(1+x-1/x)e^(x+1/x)dx is ...

The integral `int(1+x-1/x)e^(x+1/x)dx` is equal to

A

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

B

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

C

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

D

`xe^(x+(1)/(x))+C`

Text Solution

Verified by Experts

The correct Answer is:
d
We have , `int(1+x-(1)/(x))e^(x+(1)/(x))dx`
`=inte^(x+(1)/(x))dx+intunderset(I)(x) e^(x+(1)/(x))(1-(1)/(x^(2)))dx`
`=inte^(x+(1)/(x))dx+xe^(x+(1)/(x))-inte^(x+(1)/(x))dx+C=xe^(x+(1)/(x))+C`
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