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

Find the integral int((2+w)/(4+5ww^2))dw