Evaluate $\int\frac{8x+20}{5x^2+25x+20}dx$ I tried to solve it and got $\frac{4}{5} \ln(4+5 x+x^2)+C$ as an answer, but my online homework program says it's incorrect.  What did I do wrong?
I pulled out $\frac{4}{5}$ as a constant and saw that the numerator was the derivative of the denominator. So I put the denominator in a natural log.

$$\int \frac{8x+20}{5x^2+25x+20} dx=\int \frac{8x+20}{5(x+1)(x+4)} dx$$
$$\frac{8x+20}{5(x+1)(x+4)} =\frac{A}{5(x+1)}+\frac{B}{5(x+4)}=\frac{A(x+4)+B(x+1)}{5(x+1)(x+4)}$$
So:
$$A+B=8 \\ 4A+B=20$$
$$3A=12 \Rightarrow A=4$$
$$B=8-A=4$$
So:
$$\frac{8x+20}{5(x+1)(x+4)}=\frac{4}{5}  \frac{1}{x+1}+\frac{4}{5} \frac{1}{x+4}$$
Therefore:
$$\int \frac{8x+20}{5(x+1)(x+4)} dx=\frac{4}{5} \ln |x+1|+\frac{4}{5} \ln |x+4|+c$$
