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int(e^(x)(x-1)(x-lnx))/(x^(2))dx is equa...

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

A

`e^(x)((x-lnx)/(x))+c`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`int(e^(x)(x-1)(x-lnx))/(x^(2))dx`
`=inte^(x)((1)/(x)-(1)/(x^(2)))(ln.(e^(x))/(x))dx`
`=intln.(e^(x))/(x)d((e^(x))/(x))`
`=ln((e^(x))/(x))(e^(x))/(x)-(e^(x))/(x)+c`
`=(e^(x))/(x)(x-ln x-1)+c`
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