I need to compute this integral:

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

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