How do you solve these two examples? I'm having some trouble

Question

$$\int\frac{1-7x}{x^2-5x+6}\,dx$$ $$\int\frac{x-1}{x^3+x^2}\,dx$$ I've been trying for like an hour to no avail. Can somebody solve them step-by-step so I can correct what I'm doing wrong?

Answer 1

The partial fraction decompositions of the two integrands are as follows: $$\frac{1-7x}{x^2-5x+6}=\frac{13}{x-2}-\frac{20}{x-3}$$ $$\frac{x-1}{x^3+x^2}=\frac2x-\frac1{x^2}-\frac2{x+1}$$ Now you can just apply standard integration formulas to each component and sum them up.