True or False

Question

If F(x) and G(x) are antiderivatives of f(x), then F(x)=G(x)+C

If f'(x) = g(x) then integral g(x) dx = f(x) + C

Integral f(x) * g(x)dx = integral f(x)dx * integral g(x)dx

I have a feeling it's

False
True
True

Answer 1

As far as I know the first one is true, they differ by a constant.

yes, true

say f = x^2
g = x

then
F = (1/3) x^3 + C1
G = (1/2) x^2 + C2

integral f g dx = (1/3) x^4 + C

forget the constants for now, no need

F G = (1/6) x^5

like no way :)