Exercise
$\int\frac{-2x+7}{x^2-3x}dx$
Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((-2x+7)/(x^2-3x))dx. Rewrite the expression \frac{-2x+7}{x^2-3x} inside the integral in factored form. Rewrite the fraction \frac{-2x+7}{x\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-7}{3x}+\frac{1}{3\left(x-3\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-7}{3x}dx results in: -\frac{7}{3}\ln\left(x\right).
Find the integral int((-2x+7)/(x^2-3x))dx
Final answer to the exercise
$-\frac{7}{3}\ln\left|x\right|+\frac{1}{3}\ln\left|x-3\right|+C_0$