If f'(x) = 8x^3 + 3x^2 + 2 , find f(x) if f(0) = -5.

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We are given that f'(x) = 8x^3 + 3x^2 + 2. To find f(x) we need to find the integral of f'(x).

Int[f'(x)] = Int [ 8x^3 + 3x^2 + 2]

=> 8x^4 / 4 + 3x^3 / 3 + 2x + C

=> 2x^4 + x^3 + 2x + C

Also, f(0) = -5

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