How do I solve the integral of (10x^2)/((x+1)(x^2+1))?

Question

jamesj · Answer

You need to break it up into partial fractions.

.sam. · Answer

$$\frac{A}{x+1}+\frac{Bx+C}{x ^{2}+1}$$

anonymous · Answer

I am getting stuck on how to solve once I have broken it up, specifically. I tried solving by setting the numerator equal to the original numerator $$10x^2 = A(x^2+1) + (Bx+C)(x+1)$$
But all the coefficients are 0 other than 10x squared

jamesj · Answer

Yes, what you have is a system of linear equations in A, B and C.  But not all of A, B and C are zero.

anonymous · Answer

Essentially I am getting confused because to evaluate for x^0, I get A+B+C, for x^1 I get just C, and for x^2 I get A+B. Since C has to be zero, how do I accommodate to make A+B+C zero?

jamesj · Answer

Your equation above is 
$$ x^2=A(x^2+1)+(Bx+C)(x+1) $$
$$ = (A+B)x^2 + (B + C)x + (A+C) $$
Hence
A + B = 1
B + C = 0
A + C = 0

anonymous · Answer

Oh wow, I can't believe I missed something so simple :P Thank you very much