Final answer to the problem
Step-by-step Solution
Specify the solving method
Expand the fraction $\frac{x-6}{x^2-2x}$ into $2$ simpler fractions with common denominator $x^2-2x$
Learn how to solve problems step by step online.
$\int\left(\frac{x}{x^2-2x}+\frac{-6}{x^2-2x}\right)dx$
Learn how to solve problems step by step online. Find the integral int((x-6)/(x^2-2x))dx. Expand the fraction \frac{x-6}{x^2-2x} into 2 simpler fractions with common denominator x^2-2x. Expand the integral \int\left(\frac{x}{x^2-2x}+\frac{-6}{x^2-2x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Rewrite the expression \frac{x}{x^2-2x} inside the integral in factored form. The integral \int\frac{1}{x-2}dx results in: \ln\left(x-2\right).