What is the integral of x^4ln(x^3) ?

The integral of x^4ln(x^3) is 3/5 x^5ln(x)-(3x^5)/(25)+C

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integral of x^4ln(x^3)

\int x^{4} ln (x^{3}) d x

\frac{3}{5} x^{5} ln (x) - \frac{3 x ^{5}}{25} + C

Solution steps

\int x^{4} ln (x^{3}) d x

Apply Integration By Parts

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

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

\int \frac{3 x ^{4}}{5} d x = \frac{3 x ^{5}}{25}

= \frac{1}{5} x^{5} ln (x^{3}) - \frac{3 x ^{5}}{25}

\frac{1}{5} x^{5} ln (x^{3}) = \frac{3}{5} x^{5} ln (x)

= \frac{3}{5} x^{5} ln (x) - \frac{3 x ^{5}}{25}

Add a constant to the solution

= \frac{3}{5} x^{5} ln (x) - \frac{3 x ^{5}}{25} + C

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What is the integral of x^4ln(x^3) ?
The integral of x^4ln(x^3) is 3/5 x^5ln(x)-(3x^5)/(25)+C