I guess when you say antiderivative you mean integral because integral is opposite of derivative.
∫3sinxcosxdx = 3∫sinxcosxdx now we take that replacement: sinx = t
now we derivative
cosxdx = dt
3∫tdt = 3(t^2)/2
The answer is [tex] \frac{3}{2} * t^{2} [/tex]
