How do you evaluate the integral #int 1/(x^3-x)dx#?
This can be solved by using the method of partial fractions.
First factor the denominator completely.
Decompose the integrand.
Get the lowest common denominator between all of the terms of the decomposition.
Now that all terms have a common denominator, focus on the numerator to solve for the value of A, B, and C.
Substitute the decomposition in to the integral.
Break the integral into smaller integrals for each term
Bring out the constants
Integrate each term