What is the integral of x^3ln(6x) ?

The integral of x^3ln(6x) is 1/4 x^4ln(6x)-(x^4)/(16)+C

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integral of x^3ln(6x)

\int x^{3} ln (6 x) d x

\frac{1}{4} x^{4} ln (6 x) - \frac{x ^{4}}{16} + C

Solution steps

\int x^{3} ln (6 x) d x

Apply Integration By Parts

: \frac{1}{4} x^{4} ln (6 x) - \int \frac{x ^{3}}{4} d x

= \frac{1}{4} x^{4} ln (6 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 (6 x) - \frac{x ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} x^{4} ln (6 x) - \frac{x ^{4}}{16} + C

\frac{d}{d x} (x cos (x))

\int \frac{y - 1}{y + 4} d y

x \to 3 lim (6 x^{2})

\int 8 sec^{3} (6 x) d x

\frac{\partial}{\partial x} (3 e^{2 x} - 5 ln (y) + 7)

What is the integral of x^3ln(6x) ?
The integral of x^3ln(6x) is 1/4 x^4ln(6x)-(x^4)/(16)+C