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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(1-(1)/(x^(2)))e^(x+(1)/(x))dx`
`=int e^(x+(1)/(x))dx + xe^(x+(1)/(x))-int(d)/(dx)(x)e^(x+(1)/(x))dx`
`=int e^(x+(1)/(x))dx + xe^(x+(1)/(x))-int e^(x+(1)/(x))dx" "[therefore int(1-(1)/(x^(2)))e^(x+(1)/(x))dx = e^(x+(1)/(x))]`
`=int e^(x+(1)/(x))dx + xe^(x+(1)/(x))-int ex^(x+(1)/(x))dx = xe^(x+(1)/(x))+c`
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