Homework SourseFind the most general f Use C for the constant of the first
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
f \'\'(x) = 4x + sin x
Solution
f\'(x) = int f\"(x) = int 4x+sin(x) dx = 2x2 - cos(x) + C1
f(x) = int f\'(x) dx = int 2x2 - cos(x) + C1 dx =
2/3 x3 - sin(x) + C1x + C2
where C1 and C2 are constants.
