How do you integrate #(x^3+1)/((x^2-1)^2(x+1))# using partial fractions?
Rewrite the denominator as
Multiply both sides by the denominator:
Let x = -1:
Let x = 1:
If you continue by creating 3 equations to solve for the remaining 3 unknow values, you will find that:
This gives you two integrals:
Both integrals are trivial and found in lists of integrals.