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int(1+2x^(2)+(1)/(x))e^(x^(2)+(1)/(x))dx...

`int(1+2x^(2)+(1)/(x))e^(x^(2)+(1)/(x))dx` is equal to

A

`-x e^(x^(2)-(1)/(x))+c`

B

`x e^(x^(2)-(1)/(x))+c`

C

`(2x-1) e^(x^(2)-(1)/(x))+c`

D

`(2x+1) e^(x^(2)-(1)/(x))+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(1+2x^(2)+(1)/(x))e^(x^(2)-(1)/(x))dx`
`=int [e^(x^(2)-(1)/(x))+x(2x+(1)/(x^(2)))e^(x^(2)-(1)/(x))]dx`
`=x e^(x^(2)-(1)/(x))-int e^(x^(2)-(1)/(x))(2x+(1)/(x^(2)))x dx+int x(2x+(1)/(x^(2))) e^(x^(2)-(1)/(x))dx`
`=x e^(x^(2)-(1)/(x))+c`
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