What is the integral of x^3ln(2x) ?

The integral of x^3ln(2x) is 1/4 x^4ln(2x)-(x^4)/(16)+C

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integral of x^3ln(2x)

\int x^{3} ln (2 x) d x

\frac{1}{4} x^{4} ln (2 x) - \frac{x ^{4}}{16} + C

Solution steps

\int x^{3} ln (2 x) d x

Apply Integration By Parts

: \frac{1}{4} x^{4} ln (2 x) - \int \frac{x ^{3}}{4} d x

= \frac{1}{4} x^{4} ln (2 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 (2 x) - \frac{x ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} x^{4} ln (2 x) - \frac{x ^{4}}{16} + C

\frac{d}{d x} (\frac{3 x + 1}{x - 1})

\frac{\partial}{\partial x} (e^{x} sin (x))

n \to \infty lim (\frac{n ^{2} + 3}{n ^{3} n + n ^{\frac{5}{2}}})

\int \frac{x ^{3} + 3 x - 2}{x ^{2} - x} d x

\frac{d}{d x} (\frac{7}{x ^{7}})

What is the integral of x^3ln(2x) ?
The integral of x^3ln(2x) is 1/4 x^4ln(2x)-(x^4)/(16)+C