Question

Find f. (use c for the constant of the first antiderivative and d for the constant of the second antiderivative.) f ''(x) = 12x + sin x

Answer 1

$f''(x) = 12x + sinx$
$\text{Integrating f''(x), we get: }f'(x) = 6x^{2} - cosx + C$
$\text{Integrating f'(x), we get: } f(x) = 2x^{3} - sinx + Cx + D$