Question

Derivates and Integrals... I am missing something fundamental.

example 1: find the primitive function of
1/ (2x + 1)^2. Easy enough, substitute 2x + 1 = u
du/dx = 2

the integral for 1/u^2 du = (1/-u) * du =>
-2/(2x +1).

Second example, bear with me, the problem comes after this...

find the primitive function of (sinx)^2*cosx

sinx = u , du/dx = cosx

the integral becomes : u^2 * du/dx
Primitive function should be, atleast going from the first example, u^3/3 * du/dx. =>
(sinx^3/3) * cosx.

Thing is, the du/dx seemingly "dissapears" this time. why?