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int(logx)^(2)dx=?...

`int(logx)^(2)dx=?`

A

`(2logx)/(x)+C`

B

`(1)/(3)(logx)^(3)+C`

C

`x(logx)^(2)-2xlogx+2x+C`

D

`x(logx)^(2)-2xlogx-2x+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`I={underset(I)((logx)^(2))*underset(II)(1)}dx=(logx)^(2)*x-int(2logx)/(x)*xdx`
`=x(logx)^(2)-2intlogxdx=x(logx)^(2)-2[x(logx-1)]+C`.
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