Learn how to solve problems step by step online. Integrate the function 1/(-4+x^2) from 0 to 3. Rewrite the expression \frac{1}{-4+x^2} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(2+x\right)\left(-2+x\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int_{0}^{3}\left(\frac{-1}{4\left(2+x\right)}+\frac{1}{4\left(-2+x\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{3}\frac{-1}{4\left(2+x\right)}dx results in: -\frac{1}{4}\ln\left(5\right)+\frac{1}{4}\ln\left(2\right).

Integrate the function 1/(-4+x^2) from 0 to 3