# Step-by-step Solution

## Integral of $\frac{x^2}{\sqrt{x-1}}$ with respect to x

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$\frac{2}{5}\sqrt{\left(x-1\right)^{5}}+\frac{4}{3}\sqrt{\left(x-1\right)^{3}}+2\sqrt{x-1}+C_0$

## Step-by-step explanation

Problem to solve:

$\int_{ }^{ }\left(\frac{x^2}{\sqrt{x-1}}\right)dx$
1

Solve the integral $\int\frac{x^2}{\sqrt{x-1}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x-1 \\ du=dx\end{matrix}$
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Rewriting $x$ in terms of $u$

$x=u+1$

$\frac{2}{5}\sqrt{\left(x-1\right)^{5}}+\frac{4}{3}\sqrt{\left(x-1\right)^{3}}+2\sqrt{x-1}+C_0$
$\int_{ }^{ }\left(\frac{x^2}{\sqrt{x-1}}\right)dx$