f(x) = x^3 + 3x^2 + 5. Find (a) f ′′(x), (b) ∫f(x)dx.

(a) To find the second derivative of f(x) we must differentiate f twice.the first derivative of f is f'(x)= 3x^2 + 6xthe second derivative therefore is f''(x)= 6x +6
(b) The integral of f(x) with respect to x is ∫f(x) dx = ∫x^3 + 3x^2 + 5 dx = (x^4)/4 + (3x^3)/3 + 5x/1 + C = (x^4)/4 + x^3 + 5x + C where C is the constant of integration, C belongs to the set of real numbers.