What is the integral of ln(ax)x^3 ?

The integral of ln(ax)x^3 is 1/4 x^4ln(ax)-(x^4)/(16)+C

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integral of ln(ax)x^3

\int ln (a x) x^{3} d x

\frac{1}{4} x^{4} ln (a x) - \frac{x ^{4}}{16} + C

Solution steps

\int ln (a x) x^{3} d x

Apply Integration By Parts

: \frac{1}{4} x^{4} ln (a x) - \int \frac{x ^{3}}{4} d x

= \frac{1}{4} x^{4} ln (a x) - \int \frac{x ^{3}}{4} d x

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= \frac{1}{4} x^{4} ln (a x) - \frac{x ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} x^{4} ln (a x) - \frac{x ^{4}}{16} + C

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What is the integral of ln(ax)x^3 ?
The integral of ln(ax)x^3 is 1/4 x^4ln(ax)-(x^4)/(16)+C