Question

Find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative. ) f(x) = x(18x 4)

Answer 1

Below in bold.

Explanation:

f(x) = x(18x + 4)

f(x) = 18x^2 + 4x

Antiderivative = 18 * (x^2+1)/(2 + 1) -+4x(1+1) / (1+1) + C

= 18x^3 / 3 + 4x^2 / 2 + C

= 6x^3 + 2x^2 + C.

Checking by differentiating:

f'(x) = 6*3 x^(3-1) + 2*2x^(2-1)

= 18x^2 + 4x

= x(18 -+4)