Determine the function f(x) if f'(x)=15x^14+36x^5-2x^3?

To determine the primitive of the original function, we'll
have to determine te indefinite integral of the expression of
derivative.

We'll determine the indefinite integral
of

f'(x)=15x^14+36x^5-2x^3

Int
f'(x)dx = f(x) + C

Int
(15x^14+36x^5-2x^3)dx

We'll apply the property of the
indefinite integral, to be additive:

Int
(15x^14+36x^5-2x^3)dx = Int (15x^14)dx + Int (36x^5)dx - Int
(2x^3)dx

Int (15x^14)dx = 15*x^(14+1)/(14+1) +
C

Int (15x^14)dx = 15x^15/15 +
C

Int (15x^14)dx = x^15 + C
(1)

Int (36x^5)dx = 36*x^(5+1)/(5+1) +
C

Int (36x^5)dx = 36*x^6/6 +
C

Int (36x^5)dx = 6*x^6 + C
(2)

Int 2x^3dx = 2*x^4/4 +
C

Int 2xdx = x^4/2 + C
(3)

We'll add: (1)+(2)-(3)

Int
(15x^14+36x^5-2x^3)dx = x^15 + 6x^6 - x^4/2 + C

So, the
function is:

f(x) = x^15 + 6x^6 - x^4/2 +
C