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Integrate the following functions x (logx)^2

Answer»

SOLUTION :`int X(logx)^2 DX`
=`(logx)^2 x^2/2 -int 2 logx XX 1/x xx x^2/2 dx`
=`x^2/2 (logx)^2 - int x logx dx`
=`x^2/2 (logx)^2-[logx xx x^2/2-int 1/x x^2/2 dx]`
=`x^2/2 (logx)^2-x^2/2 (logx) +1/2 x^2/2 +c`
=`x^2/2 (logx)^2 - x^2/2 (logx)+x^4/4 +c`


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