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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

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

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

Main topic:

Integration by parts

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