Learn how to solve problems step by step online. Find the integral int((2x-1x^2)/(-2x+3x^22x^3))dx. Rewrite the expression \frac{2x-1+x^2}{-2x+3x^2+2x^3} inside the integral in factored form. Rewrite the fraction \frac{2x-1+x^2}{x\left(2x-1\right)\left(x+2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2x}+\frac{1}{5\left(2x-1\right)}+\frac{-1}{10\left(x+2\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2x}dx results in: \frac{1}{2}\ln\left(x\right).

Find the integral int((2x-1x^2)/(-2x+3x^22x^3))dx