# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int x\sqrt{x+1}dx$

Learn how to solve integrals with radicals problems step by step online.

$u=x+1$

Learn how to solve integrals with radicals problems step by step online. Calculate the integral int(x*(x+1)^0.5)dx. We can solve the integral \int x\sqrt{x+1}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify.

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