Step-by-step Solution

Integral of $\frac{x}{\left(9-x^2\right)^4}$ with respect to x

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$\frac{-\frac{1}{6}}{\left(-9+x^2\right)^{\left(2+1\right)}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x}{\left(9-x^2\right)^4}dx$
1

Solve the integral $\int\frac{x}{\left(9-x^2\right)^4}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=9-x^2 \\ du=-2xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

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

$\frac{-\frac{1}{6}}{\left(-9+x^2\right)^{\left(2+1\right)}}+C_0$
$\int\frac{x}{\left(9-x^2\right)^4}dx$