# Step-by-step Solution

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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.

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

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.

The integral diverges.

### Problem Analysis

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

### Main topic:

Definite integrals

~ 0.45 seconds