Mathematics

Problem

Let

f(x)=\frac{2x^{3}-1}{x^{2}},\quad x\neq 0.

Solve the following. a. (i) Simplify

f(x)

into a sum of elementary power functions. b. (ii) Find the most general function

F

such that

F'(x)=f(x)

. c. (iii) Show that if

F_{1}

and

F_{2}

are any two functions satisfying

F'_{1}(x)=F'_{2}(x)=f(x)

, then

F_{1}(x)-F_{2}(x)

is a constant.