Given f'(x)=25x^4+6x determine f(x).

By definition, f(x) could be determined evaluating the
indefinite integral of f'(x)

Int
(25x^4+6x)dx

We'll apply the additive property of
integrals:

Int (25x^4+6x)dx = Int (25x^4)dx + Int
(6x)dx

We'll re-write the sum of integrals, taking out the
constants:

Int (25x^4+6x)dx = 25Int x^4 dx + 6Int x
dx

Int (25x^4+6x)dx = 25*x^5/5 +
6*x^2/2

We'll simplify and we'll
get:

Int (25x^4+6x)dx = 5x^5 + 3x^2 +
C

The function f(x) is:
f(x) = 5x^5 + 3x^2 +
C