Solution: 1, f (x)' = 4x3-x (-1) f (1)' = 4-1= 32, because f (x) = ∫ 2x-e (-) Because f (x)' = 2x/4+x 2 is increasing in (-∞ +∞), the monotonic increasing interval of the function is (-∞) 4, ∫ (ln 2x/x) dx = ∫ ln 2xd (lnx) = ln 3/3+c.