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! 

Now set $x=i$ and you get 
$$Bi+C=-\frac{17}{i+1}=\frac{17}2(i-1)$$
hence you find the value of $B$ and $C$ simultaneously.
Notice that
$$\int\frac{dx}{x^2+1}=\arctan x+C$$
and
$$ \int\frac{x\,dx}{x^2+1}=\frac12\ln(x^2+1)+C$$
Can you take it from here?
