Exercise
$\int\frac{x+12}{x^2-x-6}dx$
Step-by-step Solution
Learn how to solve equations problems step by step online. Find the integral int((x+12)/(x^2-x+-6))dx. Rewrite the expression \frac{x+12}{x^2-x-6} inside the integral in factored form. Rewrite the fraction \frac{x+12}{\left(x+2\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-2}{x+2}+\frac{3}{x-3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-2}{x+2}dx results in: -2\ln\left(x+2\right).
Find the integral int((x+12)/(x^2-x+-6))dx
Final answer to the exercise
$-2\ln\left|x+2\right|+3\ln\left|x-3\right|+C_0$