Question

Find the most general f. Use C for the constant of the first anti-derivative and D for the constant of the second anti-derivative.

f ''(x) = 4x + sin x

Answer 1

first integrate this second derivative: 2x^2+cosx+D

The integrate the first derivative: 2/3x^3-sinx+C

Answer 2

\[f(x)=2x^2-\cos(x)+C\]

\[f(x)=\frac{2}{3}x^3-\sin(x)+Cx+D\]

Answer 3

the first one should be \[f'(x)\]