Evaluate the integral $$\int {\frac{4x^3-27x^2+5x-32}{30x^5-13x^4+50x^3-286x^2-299x-70}}\, dx.$$ by using a computer algebra system to find the partial fraction decomposition of the integrand and then computing the resulting integral by hand.

Note: Use an upper-case "C" for the constant of integration.