Final answer to the problem
Step-by-step Solution
Specify the solving method
Expand the fraction $\frac{x-8}{x^2+2}$ into $2$ simpler fractions with common denominator $x^2+2$
Learn how to solve problems step by step online.
$\int\left(\frac{x}{x^2+2}+\frac{-8}{x^2+2}\right)dx$
Learn how to solve problems step by step online. Find the integral int((x-8)/(x^2+2))dx. Expand the fraction \frac{x-8}{x^2+2} into 2 simpler fractions with common denominator x^2+2. Expand the integral \int\left(\frac{x}{x^2+2}+\frac{-8}{x^2+2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Rewrite the fraction \frac{x}{x^2+2} inside the integral as the product of two functions: x\frac{1}{x^2+2}. We can solve the integral \int x\frac{1}{x^2+2}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.