Step-by-step Solution

Integrate $x^3e^{-2x}$ from $0$ to $\infty $

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Step-by-step explanation

Problem to solve:

$\int_0^{\infty}\left(x^3e^{-2x}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\lim_{c\to\infty }\:\int_{0}^{c} x^3e^{-2x}dx$

Unlock this full step-by-step solution!

Learn how to solve definite integrals problems step by step online. Integrate x^3e^(-2x) from 0 to \infty. Replace the integral's limit by a finite value. Use the integration by parts theorem to calculate the integral \int x^3e^{-2x}dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final Answer

The integral diverges.

Problem Analysis