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

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

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integral of (x^3ln(x))

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

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

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

\int \frac{a ^{x}}{x} d x

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\frac{d}{d y} (e^{y} + \frac{y}{x})

\int cot^{4} (x cs) c^{2} x d x

\int cot^{3} (θ) csc^{2} (θ) d θ

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