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

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

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integral of x^4*ln(x)

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

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

Solution steps

\int x^{4} ln (x) 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

\int \frac{i}{x} d x

\frac{d}{d x} (ln (x^{2} - 10 x))

\frac{\partial}{\partial x} (e^{- \frac{x}{a}})

\frac{\partial}{\partial y} (2 x + 3 y - 4)

\frac{\partial}{\partial y} (e^{x} y^{3} + 2 y e^{2 x})

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