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\int\left(x^2\ln\left(x\right)\right)dx

Integrate x^2ln(x)

Answer

$-\frac{1}{5}x^{5}+\frac{x^{3}\ln\left(x\right)}{3}+C_0$

Step-by-step explanation

Problem

$\int\left(x^2\ln\left(x\right)\right)dx$
1

Use the integration by parts theorem to calculate the integral $\int x^2\ln\left(x\right)dx$, using the following formula

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

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Answer

$-\frac{1}{5}x^{5}+\frac{x^{3}\ln\left(x\right)}{3}+C_0$