What is the integral of x^3ln(x^5) ?

The integral of x^3ln(x^5) is 5/4 x^4ln(x)-(5x^4)/(16)+C

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integral of x^3ln(x^5)

\int x^{3} ln (x^{5}) d x

\frac{5}{4} x^{4} ln (x) - \frac{5 x ^{4}}{16} + C

Solution steps

\int x^{3} ln (x^{5}) d x

Apply Integration By Parts

= \frac{1}{4} x^{4} ln (x^{5}) - \int \frac{5 x ^{3}}{4} d x

\int \frac{5 x ^{3}}{4} d x = \frac{5 x ^{4}}{16}

= \frac{1}{4} x^{4} ln (x^{5}) - \frac{5 x ^{4}}{16}

\frac{1}{4} x^{4} ln (x^{5}) = \frac{5}{4} x^{4} ln (x)

= \frac{5}{4} x^{4} ln (x) - \frac{5 x ^{4}}{16}

Add a constant to the solution

= \frac{5}{4} x^{4} ln (x) - \frac{5 x ^{4}}{16} + C

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What is the integral of x^3ln(x^5) ?
The integral of x^3ln(x^5) is 5/4 x^4ln(x)-(5x^4)/(16)+C