f(x) = [3/x^2] - [5/x^7], F(x) is the antiderivative of f(x) with F(1)=0.

Question

F(x) = ?

I have no idea how to approach this problem. The fractions are scaring me.

Answer 1

This is really pretty simple, I can't imagine how you are stuck.

INTf(x)= INT 3x^-2 dx -INT (5x^-7)dx
= -3x^-1 +5/6 x^-6 +C
F(1)=0 = -3+5/6+C=1
solve for C.
F(x) = -3x^-1 +5/6 x^-6 check my work, it is easy to make a typo