# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\left(X\left(1+X\right)^{\left(1/2\right)}\right)dx$

Learn how to solve calculus problems step by step online.

$\begin{matrix}u=1+x \\ du=dx\end{matrix}$

Learn how to solve calculus problems step by step online. Calculate the integral of int(x*(1+x)^((1/2)))dx. Solve the integral \int x\sqrt{1+x}dx applying u-substitution. Let u and du be. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify. Multiplying polynomials \sqrt{u} and u-1.

$\frac{2}{5}\sqrt{\left(1+x\right)^{5}}-\frac{2}{3}\sqrt{\left(1+x\right)^{3}}+C_0$

### Problem Analysis

$\int\left(X\left(1+X\right)^{\left(1/2\right)}\right)dx$

Calculus

~ 1.29 seconds
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