# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

Learn how to solve integrals of rational functions problems step by step online. Integral of (x^2)/((x^2-4)^0.5) with respect to x. Add and subtract -4. Split the integral in two integrals. Simplify the fraction by x^2-4. The integral \int\sqrt{x^2-4}dx results in: \frac{1}{2}x\sqrt{x^2-4}.

$2\ln\left|\frac{x+\sqrt{x^2-4}}{2}\right|+\frac{1}{2}x\sqrt{x^2-4}+C_0$

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 0.44 seconds