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Step-by-step Solution

Integral of $x^2\sqrt{x-4}$

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Answer

$\frac{2}{7}\sqrt{\left(x-4\right)^{7}}+\frac{16}{5}\sqrt{\left(x-4\right)^{5}}+\frac{32}{3}\sqrt{\left(x-4\right)^{3}}+C_0$

Step-by-step explanation

Problem to solve:

$\int x^2\sqrt{x-4}dx$
1

Solve the integral $\int x^2\sqrt{x-4}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x-4 \\ du=dx\end{matrix}$
2

Rewriting $x$ in terms of $u$

$x=u+4$

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Answer

$\frac{2}{7}\sqrt{\left(x-4\right)^{7}}+\frac{16}{5}\sqrt{\left(x-4\right)^{5}}+\frac{32}{3}\sqrt{\left(x-4\right)^{3}}+C_0$

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