Since cos(x) is the derivative of sin(x), then 12 sin(x) cos(x) dx can be done by substituting u = Step 4 With the substitution u = sin(x), we get 12 12 sin(x) cos(x) dx = 12 12/u2 du. which integrates to X + C. Substituting back in to get the answer in terms of sin(x), we have 12 sin(x) cos(x) dx = || + C. sin(x)