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. $\backslash$int z$^3\backslash$ln z $\backslash$hbox$\{$d$\}$ z $=\backslash$int e$^$t $\backslash$cos t $\backslash$hbox$\{$d$\}$ t $=\backslash$int$\_0^\{2\backslash$pi$\}\backslash$sin$($x$)\backslash$sin$($x$+1)\backslash$hbox$\{$d$\}$ x $=$