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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

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
a
Let `I=int(1+x-x^(-1))e^(x+x^(-1))` dx. then,
`I=inte^(x+x^(-1))dx =intunderset((I))(x)underset(II)((1-(1)/(x^(2))))e^(x+(1)/(x))dx`
`rArr I=inte^(x+x^(-1))dx+xe^(x+(1)/(x))-inte^(x+x^(-1))dx+C`
`rArrI=xe^(x+x^(-1))+C`
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