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int(1+x-x^(- 1))e^(x+x^(- 1))dx=...

`int(1+x-x^(- 1))e^(x+x^(- 1))dx=`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Let `I=int(1+x-x^(-1))e^(x+x^(-1))dx`
`rArrI=inte^(x+x^(-1))dx+intx(1-(1)/(x^(2)))e^(x+x^(-1))dx`
`rArr I=inte^(x+x^(-1))dx+intunderset(I)(x)e^(x+x^(-1))d(x+x^(-1))`
`rArr I=inte^(x+x^(-1))dx+xe^(x+x^(-1))-inte^(x+x^(-1))dx`
`rArrI=xe^(x+x^(-1))+C`
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