how do you integrate 30x^2/(x-2)(x+3)(x-5)

Answer 1

With partial fractions. Use the method we have shown you in some of your previous questions

A/(x-2) + B/(x+3) + C(x-5)
= 30x^2/[(x-2)(x+3)(x-5)]

= A(x+3)(x-5)+B(x-2)(x-5)+C(x-2)(x+3)/[(x-2)(x+3)(x-5)]

Solve for A, B and c and integrate the separate terms