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Question
Evaluate the following : `int x^3.logx.dx`
Solution
Let I =`int x^3.logx.dx`
= `int log x.x^3.dx`
= `(logx) int x^3.dx - int[{d/dx (logx) int x^3.dx}].dx`
= `(logx).x^4/(4) - int (1)/x.x^4/(4).dx`
= `x^4/(4) logx - (1)/(4) int x^3.dx`
= `x^4/(4) logx - (1)/(4)(x^4/4) + c`
= `x^4/(4) logx - x^4/(16) + c`.
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