inte^(x)((x-1)(x-logx))/(x^(2))dx is equ...

`inte^(x)((x-1)(x-logx))/(x^(2))dx` is equal to

A

`e^(x)((x-"In "x)/(x))+C`

B

`e^(x)((x-"In "x+1)/(x))+C`

C

`e^(x)((x-"In "x)/(x))+C`

D

`e^(x)((x-"In "x-1)/(x))+C`

Text Solution

Verified by Experts

The correct Answer is:

d

Let `I=inte^(x)((x-1)(x-log))/(x^(2))dx` . Then ,
`I=inte^(x)((x^(2)-x+logx-xlogx)/(x^(2)))dx`
`rArrI=inte^(x)((x-logx-1)/(underset(f)(x))+(logx)/(underset(f')(x^(2))))dx`
`rArrI=e^(x)((x-logx-1)/(x))+C`

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