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Question
Evaluate the following : `int x^2.log x.dx`
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Solution
Let I = `int x^2.logx.dx`
= `int log x.x^2.dx`
= `(logx) int x^2.dx - int[{d/dx (logx) int x^2.dx}].dx`
= `(logx).x^3/(3) - int (1)/x.x^3/(3).dx`
= `x^3/(3) logx - (1)/(3) int x^2.dx`
= `x^3/(3) logx - (1)/(3)(x^3/3) + c`
= `x^3/(9)(3.logx - 1) + c`.
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