# Integral of ln(y)y^3

## Answer

$y^3\left(y\ln\left(y\right)-y\right)-3\int y^{2}\left(y\ln\left(y\right)-y\right)dy$

## Step-by-step explanation

Problem

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

1

Use the integration by parts theorem to calculate the integral $\int u\cdot y^{4}du$, using the following formula

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

## Answer

$y^3\left(y\ln\left(y\right)-y\right)-3\int y^{2}\left(y\ln\left(y\right)-y\right)dy$