# Math virtual assistant

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# Step-by-step Solution

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## Answer

$\frac{x^{3}}{3}\ln\left(x\right)-\frac{1}{9}x^{3}+C_0$

## Step-by-step explanation

Problem to solve:

$\int x^2\:\ln\:x\:dx$
1

Any expression multiplied by $1$ is equal to itself

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

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

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

## Answer

$\frac{x^{3}}{3}\ln\left(x\right)-\frac{1}{9}x^{3}+C_0$
$\int x^2\:\ln\:x\:dx$

### Main topic:

Trigonometric integrals

~ 1.19 seconds

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