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int x log x dx is equal to...

`int x log x dx` is equal to

A

`(x^(2))/(4)(2log x - 1)+C`

B

`(x^(2))/(2)(2logx-1)+C`

C

`(x^(2))/(4)(2logx+1)+C`

D

`(x^(2))/(2)(2logx+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`int underset("II")(x)underset("I")(log)x dx=logx.(x^(2))/(2)-int(1)/(x).(x^(2))/(2)dx`
Using integration parts, we get
`=(x^(2))/(2)log x-(1)/(2)(x^(2))/(2)+C=(x^(2))/(4)(2log x-1)+C`
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