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# Integral of x(x^2)/((16-1x^2)^0.5)

### Formulas

$16\int\frac{\sin\left(\theta\right)^{3}\cdot\frac{d}{d\theta}\left(4\sin\left(\theta\right)\right)}{\cos\left(\theta\right)}d\theta$

## Step-by-step explanation

Problem

$\int x\cdot \frac{x^2}{\sqrt{16-x^2}}dx$
1

Solve the integral $\int x\frac{x^2}{\sqrt{16-x^2}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=4\sin\left(\theta\right) \\ dx=\frac{d}{d\theta}\left(4\sin\left(\theta\right)\right)d\theta\end{matrix}$

$16\int\frac{\sin\left(\theta\right)^{3}\cdot\frac{d}{d\theta}\left(4\sin\left(\theta\right)\right)}{\cos\left(\theta\right)}d\theta$

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$\int x\cdot \frac{x^2}{\sqrt{16-x^2}}dx$

### Main topic:

Integration by trigonometric substitution

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