# Step-by-step Solution

## Integral of 1/(x^2(4-x^2)^0.5)

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### Videos

$\frac{-\frac{1}{4}\sqrt{4-x^2}}{x}+C_0$

## Step-by-step explanation

Problem to solve:

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

Solve the integral $\int\frac{1}{x^2\sqrt{4-x^2}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=2\sin\left(\theta\right) \\ dx=2\cos\left(\theta\right)d\theta\end{matrix}$
2

Substituting in the original integral, we get

$\int\frac{2\cos\left(\theta\right)}{4\sin\left(\theta\right)^2\sqrt{4-4\sin\left(\theta\right)^2}}d\theta$

$\frac{-\frac{1}{4}\sqrt{4-x^2}}{x}+C_0$
$\int\frac{1}{x^2\sqrt{4-x^2}}dx$

### Main topic:

Integration by trigonometric substitution

~ 2.26 seconds

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