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Step-by-step Solution

Integral of $\frac{x}{\left(1-x^2\right)^{\left(\frac{5}{2}\right)}}$ with respect to x

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Answer

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

Step-by-step explanation

Problem to solve:

$\int\left(\frac{x}{\left(1-x^2\right)^{\frac{5}{2}}}\right)dx$
1

Solve the integral $\int\frac{x}{\sqrt{\left(1-x^2\right)^{5}}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=1-x^2 \\ du=-2xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{-2x}=dx$

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Answer

$\frac{\frac{1}{3}}{\sqrt{\left(1-x^2\right)^{3}}}+C_0$
$\int\left(\frac{x}{\left(1-x^2\right)^{\frac{5}{2}}}\right)dx$

Main topic:

Integrals of Rational Functions

Used formulas:

2. See formulas

Time to solve it:

~ 1.27 seconds