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Step-by-step Solution

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

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Answer

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

Step-by-step explanation

Problem to solve:

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

Calculate the power

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

Solve the integral $\int\frac{x}{\sqrt{4-x^2}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=4-x^2 \\ du=-2xdx\end{matrix}$

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Answer

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