Partial Fraction problem has me scratching more than my head

[quazzimotto]

Problem: integrate 4x^2 / (x^2+1)^2
partial fractions?
Finding LCD and cross multiply:
Note : Quadratic

4x^2 / (x^2+1)^2 = Ax+B / (x^2+1) + Cx+D / (x^2+1)^2

4x^2 = Ax+B(x^2+1) + Cx + D

factored out:

4x^2 = Ax^3 + Ax + Bx^2 + B + Cx + D

eq Like Terms:

Here is were I'm stuck .... gathered like terms
x^3 : 0 = A
x^2: 4 = B
X^1: 0 = A+C
X^0: 0 = D


Int 4x^2 / (x^2+1)^2 = int 4 / (x^2+1) ?
Seems I should have another term here?

what did I do wrong and what is equivalent partial fraction to original problem?

thanks

 

[Count Iblis]

In this case you could just rewrite the numerator:


x^2 = x^2 + 1 - 1.

Then the fraction becomes:

4/(x^2 + 1) - 4/(x^2+1)^2

Both terms are easily integrated.

 

[quazzimotto]

Thanks!