Learn how to solve integrals of rational functions problems step by step online. Integrate the function x/(x^2-4) from 0 to 3/2. Rewrite the expression \frac{x}{x^2-4} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(x+2\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int_{0}^{\frac{3}{2}}\left(\frac{1}{2\left(x+2\right)}+\frac{1}{2\left(x-2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{\frac{3}{2}}\frac{1}{2\left(x+2\right)}dx results in: \frac{1}{2}\ln\left(\frac{7}{2}\right)-\frac{1}{2}\ln\left(2\right).

Integrate the function x/(x^2-4) from 0 to 3/2