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Step-by-step Solution

Integral of $\frac{x}{\sqrt{81-x^2}}$ with respect to x

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Answer

$-\sqrt{81-x^2}+C_0$

Step-by-step explanation

Problem to solve:

$\int\:\frac{x\:dx}{\sqrt{81-x^2}}$
1

Solve the integral $\int\frac{x}{\sqrt{81-x^2}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=81-x^2 \\ du=-2xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

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

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Answer

$-\sqrt{81-x^2}+C_0$
$\int\:\frac{x\:dx}{\sqrt{81-x^2}}$

Main topic:

Integrals of Rational Functions

Used formulas:

4. See formulas

Time to solve it:

~ 0.91 seconds

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