# Step-by-step Solution

## Integral of $\frac{1}{\sqrt{\left(1+x^2\right)^3}}$ with respect to x

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### Videos

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

## Step-by-step explanation

Problem to solve:

$\int\frac{1}{\sqrt{\left(1+x^2\right)^3}}dx$
1

Applying the power of a power property

$\int\frac{1}{\sqrt{\left(1+x^2\right)^{3}}}dx$
2

Solve the integral $\int\frac{1}{\sqrt{\left(1+x^2\right)^{3}}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=1\tan\left(\theta\right) \\ dx=\sec\left(\theta\right)^2d\theta\end{matrix}$

$\frac{x}{\sqrt{1+x^2}}+C_0$
$\int\frac{1}{\sqrt{\left(1+x^2\right)^3}}dx$

### Main topic:

Integrals of Rational Functions

~ 1.0 seconds