Final answer to the problem
Step-by-step Solution
Specify the solving method
Expand the integral $\int\left(2x+\frac{x+5}{x^2-2x-8}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
Learn how to solve problems step by step online.
$\int2xdx+\int\frac{x+5}{x^2-2x-8}dx$
Learn how to solve problems step by step online. Integrate int(2x+(x+5)/(x^2-2x+-8))dx. Expand the integral \int\left(2x+\frac{x+5}{x^2-2x-8}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2xdx results in: x^2. The integral \int\frac{x+5}{x^2-2x-8}dx results in: -\frac{1}{2}\ln\left(x+2\right)+\frac{3}{2}\ln\left(x-4\right). Gather the results of all integrals.