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

The integral of ln(x)*x^4 is 1/5 x^5ln(x)-(x^5)/(25)+C

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integral of ln(x)*x^4

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

\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25} + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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What is the integral of ln(x)*x^4 ?
The integral of ln(x)*x^4 is 1/5 x^5ln(x)-(x^5)/(25)+C