Exercise
$\int\frac{x^2+2}{x^3-6x}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^2+2)/(x^3-6x))dx. Rewrite the expression \frac{x^2+2}{x^3-6x} inside the integral in factored form. Rewrite the fraction \frac{x^2+2}{x\left(x^2-6\right)} in 2 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{-1}{3x}dx results in: -\frac{1}{3}\ln\left(x\right).
Find the integral int((x^2+2)/(x^3-6x))dx
Final answer to the exercise
$-\frac{1}{3}\ln\left|x\right|+\frac{4}{3}\ln\left|\sqrt{x^2-6}\right|+C_1$