# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

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

Learn how to solve integrals of rational functions problems step by step online. Integral of x/((81-x^2)^0.5) with respect to x. Solve the integral \int\frac{x}{\sqrt{81-x^2}}dx applying u-substitution. Let u and du be. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify. Take the constant out of the integral.

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 0.97 seconds