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Step-by-step Solution

Integral of x^2e^x

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Answer

$e^x\cdot x^2-2\left(e^x\cdot x-e^x\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int_{ }^{ }x^2\left(e^x\right)dx$
1

Use the integration by parts theorem to calculate the integral $\int x^2e^xdx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=x^2}\\ \displaystyle{du=2xdx}\end{matrix}$

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Answer

$e^x\cdot x^2-2\left(e^x\cdot x-e^x\right)+C_0$
$\int_{ }^{ }x^2\left(e^x\right)dx$

Main topic:

Integration by parts

Used formulas:

4. See formulas

Time to solve it:

~ 0.48 seconds