Integration by Parts: This is the most important integration technique we've discussed in this class. It has a wide range of applications beyond increasing our list of integration rules.
$\int z^3 \ln z \hbox{d} z =$ .
$\int e^t \cos t \hbox{d} t =$ .
$\int_0^{2\pi} \sin(x) \sin(x+1) \hbox{d} x =$.