Learn how to solve problems step by step online. Find the integral int((2y^2+y)/(4y^3+3y^2-y))dy. Rewrite the expression \frac{2y^2+y}{4y^3+3y^2-y} inside the integral in factored form. Rewrite the expression \frac{2y^2+y}{y\left(4y-1\right)\left(y+1\right)} inside the integral in factored form. Rewrite the fraction \frac{2y+1}{\left(4y-1\right)\left(y+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{6}{5\left(4y-1\right)}+\frac{1}{5\left(y+1\right)}\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Find the integral int((2y^2+y)/(4y^3+3y^2-y))dy