Step-by-step Solution

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Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of exponential functions problems step by step online.

$\begin{matrix}P(x)=y^2 \\ T(x)=e^{2y}\end{matrix}$

Learn how to solve integrals of exponential functions problems step by step online. Compute the integral int(y^2*2.718281828459045^(2*y))dy. We can solve the integral \int y^2e^{2y}dy by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x). With the derivatives and integrals of both functions we build the following table.

$\frac{1}{2}y^2e^{2y}-\frac{1}{2}ye^{2y}+\frac{1}{4}e^{2y}+C_0$
$\int y^2 e^{2y}dy$