# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\left(x^{3\:}+2\right)^{\frac{1}{2}}x\:^2dx$

Learn how to solve calculus problems step by step online.

$\begin{matrix}u=x^3+2 \\ du=3x^{2}dx\end{matrix}$

Learn how to solve calculus problems step by step online. Integrate int((x^3+2)^((1/2))*x^2)dx with respect to x. Solve the integral \int x^2\sqrt{x^3+2}dx applying u-substitution. Let u and du be. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify. Take the constant out of the integral.

$\frac{2}{9}\sqrt{\left(x^3+2\right)^{3}}+C_0$

### Problem Analysis

$\int\left(x^{3\:}+2\right)^{\frac{1}{2}}x\:^2dx$

Calculus

~ 0.04 seconds