We have f'(x) = 25x^4 + 2e^2x

f(x) = Int [ f'(x) dx]

=> f(x) = Int[ 25x^4 + 2e^2x dx]

=> f(x) = Int [ 25 x^4 dx] + Int [ 2e^2x dx]

=> f(x) = 25* x^5 / 5 + 2*e^2x/2 + C

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

**The required integral is 5x^5 + e^2x + C**

We have f'(x) = 25x^4 + 2e^2x

f(x) = Int [ f'(x) dx]

=> f(x) = Int[ 25x^4 + 2e^2x dx]

=> f(x) = Int [ 25 x^4 dx] + Int [ 2e^2x dx]

=> f(x) = 25* x^5 / 5 + 2*e^2x/2 + C

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

**The required integral is 5x^5 + e^2x + C**