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

Integrate x^2(x-4)^0.5

Answer

$8\left(x-4\right)^{4}+\frac{2}{7}\sqrt{\left(x-4\right)^{7}}+256+x\left(16x-128\right)+C_0$

Step-by-step explanation

Problem

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

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

$\begin{matrix}u=\sqrt{x-4} \\ du=\frac{1}{2}\left(x-4\right)^{-\frac{1}{2}}dx\end{matrix}$

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Answer

$8\left(x-4\right)^{4}+\frac{2}{7}\sqrt{\left(x-4\right)^{7}}+256+x\left(16x-128\right)+C_0$

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