# Integrate ln(y)y^3

## Answer

$\frac{y^{4}\ln\left(y\right)}{4}-\frac{1}{7}y^{7}+C_0$

## Step-by-step explanation

Problem to solve:

$\int\ln\left(y\right)y^3dy$

1

Use the integration by parts theorem to calculate the integral $\int y^3\ln\left(y\right)dy$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

## Answer

$\frac{y^{4}\ln\left(y\right)}{4}-\frac{1}{7}y^{7}+C_0$