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intx(x^x)^x(2logx+1)dx=...

`intx(x^x)^x(2logx+1)dx=`

A

`(x^(x))^(x)+C`

B

`x^(x)+C`

C

`x^(logx)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=intx(x^(x))^(x)(2log x+1)dx`
`"Let "(x^(x))^(x)=t, x^(2)log x= log t`
`rArr" "(x^(2).(1)/(x)+2xlogx)d=(1)/(t)dt`
`rArr" "x(1+2logx)dx=(1)/(t)dt`
`therefore" "l=int t.(1)/(t)dt= t +C=(x^(x))^(x)+C`
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