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\int x^2 e^{-2x}dx

Integrate x^2e^(-2x)

Answer

$-\frac{1}{2}x^2e^{-2x}-\int-\frac{1}{2}e^{-2x}\cdot\frac{d}{dx}\left(x^2\right)dx$

Step-by-step explanation

Problem

$\int x^2 e^{-2x}dx$
1

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

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

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Answer

$-\frac{1}{2}x^2e^{-2x}-\int-\frac{1}{2}e^{-2x}\cdot\frac{d}{dx}\left(x^2\right)dx$

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$\int x^2 e^{-2x}dx$

Main topic:

Integration by parts

Used formulas:

1. See formulas

Time to solve it:

~ 3.2 seconds