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Step-by-step Solution

Compute the integral $\int x^2e^{-3x}dx$

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Step-by-step explanation

Problem to solve:

$\int\:x^2\:e^{-3x}dx$

Learn how to solve limits by direct substitution problems step by step online.

$\begin{matrix}u=e^{-3x} \\ du=-3e^{-3x}dx\end{matrix}$

Unlock this full step-by-step solution!

Learn how to solve limits by direct substitution problems step by step online. Compute the integral int(x^2*2.718281828459045^(-3*x))dx. Solve the integral \int x^2e^{-3x}dx applying u-substitution. Let u and du be. Isolate dx in the previous equation. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify.

Answer

$-\frac{1}{27}\left(e^{-3x}\left(-3x\right)^2-2\left(-3e^{-3x}x-e^{-3x}\right)\right)+C_0$

Problem Analysis