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Step-by-step Solution

Integral of $y^2e^{2y}$

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Answer

$\frac{1}{2}e^{2y}y^2-\left(\frac{1}{2}e^{2y}y-\frac{1}{4}e^{2y}\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int y^2 e^{2y}dy$
1

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

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

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=y^2}\\ \displaystyle{du=2ydy}\end{matrix}$

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Answer

$\frac{1}{2}e^{2y}y^2-\left(\frac{1}{2}e^{2y}y-\frac{1}{4}e^{2y}\right)+C_0$
$\int y^2 e^{2y}dy$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.78 seconds

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