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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:
B
`int(1+x-(1)/(x))e^((x+(1)/(x)))dx`
`=int e^((x+(1)/(x)))dx+int x(1-(1)/(x^(2)))e^((x+(1)/(x)))dx+c`
`=int e^((x+(1)/(x)))dx+xe^((x+(1)/(x)))-int e^((x+(1)/(x)))dx+c`
`" "`(integrating second integral using by parts)
`=xe^((x+(1)/(x)))+c`
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