What is f(x) if f'(x)=25x^4+2e^2x ?

To calculate a function, when knowing it's derivative,
we'll have to integrate the expression of derivative.

We'll
determine the indefinite integral of f'(x)=
25x^4+2e^2x.

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

Int (25x^4+2e^2x)dx

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

Int (25x^4+2e^2x)dx  =Int (25x^4)dx + Int
(2e^2x)dx 

Int (25x^4)dx = 25*x^(4+1)/(4+1) +
C

Int (25x^4)dx = 25x^5/5 +
C

Int (25x^4)dx = 5x^5 + C
(1)

Int 2e^2xdx = 2*e^2x/2 +
C

Int 2e^2xdx = e^2x + C
(2)

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

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

So, the function
is:

f(x) = 5x^5 + e^2x +
C