Evaluate the following : ∫x3.logx.dx - Mathematics and Statistics

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Sum

Evaluate the following : `int x^3.logx.dx`

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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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Chapter 3: Indefinite Integration - Exercise 3.3 [Page 137]

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