Partial Fractions I am working on some online calculus 2 partial fraction problems and I just can not seem to do this one. The question reads: "Evaluate the integral $\int \frac{17x^2}{(x+1)(x^2+1)}\, dx$."
I approached the problem by setting $\frac{17x^2}{(x+1)(x^2+1)}= \frac{A}{x+1} +\frac{Bx+C}{x^2+1}$. I then set $x=-1$ and solved for $A$ to get $A=17/2$. Wolframalpha was able to give me the correct answer to be: $(-17/4)(-\ln|x^2+1|-2\ln|x+1|+2\arctan(x))$, but I am not completely sure how they arrived  at that answer after solving for A. I would be so grateful if someone could help walk me through the rest of this problem. Thank you! 

Okay, we've found $A = \dfrac{17}2$.
We also know  $$A(x^2 + 1) + (Bx + C) (x + 1) = 17x^2$$
Now, if you want to stick with real valued $x$, first let $x = 0$
Then $$\underbrace{\frac{17}2}_{A} + C = 0 \iff C = -\frac{17}{2}$$
Now, let $x = 1$:
$$\underbrace{17}_{2A}+ 2B + 2C = 17 \iff 2B + 2C = 0 \iff B = -C = \frac{17}{2}$$
