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 (x^{3} + 1)^{2} x^{2} d x

(x + 1) y^{^{'}} + (x + 2) y = 2 x e^{- x}

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 10, (27, 1)

\frac{d}{d x} (2 x^{3} - 3 x^{2} + 2 x)

6 x^{4} - 9 x y - 7 y^{2} = 104, (- 2, 2)

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