Learn how to solve problems step by step online. Find the integral int(s/((s^2+16)(s^2+6s+9)))ds. Rewrite the expression \frac{s}{\left(s^2+16\right)\left(s^2+6s+9\right)} inside the integral in factored form. Rewrite the fraction \frac{s}{\left(s^2+16\right)\left(s+3\right)^{2}} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{3}{268}s+\frac{47}{306}}{s^2+16}+\frac{-3}{25\left(s+3\right)^{2}}+\frac{3}{268\left(s+3\right)}\right)ds into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-\frac{3}{268}s+\frac{47}{306}}{s^2+16}ds results in: \frac{3}{268}\ln\left(\frac{4}{\sqrt{s^2+16}}\right)+\frac{47}{1224}\arctan\left(\frac{s}{4}\right).

Find the integral int(s/((s^2+16)(s^2+6s+9)))ds