<s>[INST] 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.
 [/INST] Substitute $u=5x^2+25x+20$, $du=10x+25$, then$$\int\frac{8x+20}{5x^2+25x+20}dx=\frac {4}{5} \int \frac {1}{u} du = \frac{4}{5} \ln|5(x^2+5x+4)|+C.$$
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