Integrate the function $\frac{2x}{x^2-4}$ from $1$ to $3$

Learn how to solve problems step by step online.

$\int_{1}^{2}\frac{2x}{x^2-4}dx+\int_{2}^{3}\frac{2x}{x^2-4}dx$

Learn how to solve problems step by step online. Integrate the function (2x)/(x^2-4) from 1 to 3. Since the integral \int_{1}^{3}\frac{2x}{x^2-4}dx has a discontinuity inside the interval, we have to split it in two integrals. Simplify the expression inside the integral. The integral 2\int_{1}^{2}\frac{x}{x^2-4}dx results in: \lim_{c\to2}\left(-2\ln\left(\frac{2}{\sqrt{c^2-4}}\right)+2\ln\left(\frac{2}{\sqrt{-3}}\right)\right). The integral 2\int_{2}^{3}\frac{x}{x^2-4}dx results in: \lim_{c\to2}\left(\ln\left(\frac{5}{4}\right)+2\ln\left(\frac{2}{\sqrt{c^2-4}}\right)\right).