# I need help with integration using partial fractions

1. Sep 25, 2009

### farisallil

1. The problem statement, all variables and given/known data

Compute the integral:
int ((1-x^2)/(x^3+x)) dx

2. Relevant equations
int ((1-x^2)/(x^3+x)) dx

3. The attempt at a solution
I think I should use the partial fraction method to simplify the fraction
so
(1-x^2)/(x^3+x)= A/x + B/ (1+x^2)
Therefore
A(1+x^2)+B(x)=1-x^2
putting it in a polynomial form:
x^2 (A)+x (B) + 1 (A)= 1- x^2
and by equating the coefficients,
A = -1
B = 0
However, A doesn't satisfy the constant on the LHS (+1)

So what is the thing that I did wrong??

Thanks in advance

2. Sep 25, 2009

### lanedance

I think you missed the quadratic part of your partial fraction decomposition, it should be

$$\frac{1-x^2}{x(1+x^2)}= \frac{A}{x}+\frac{B+Cx}{1+x^2}$$

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