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
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