Deduce that:
$$\int _ { 0 } ^ { + \infty } ( \cos ( t ) ) ^ { 2 p } \frac { \sin ( t ) } { t } \mathrm {~d} t = \int _ { 0 } ^ { \frac { \pi } { 2 } } ( \cos ( t ) ) ^ { 2 p } \mathrm {~d} t$$
In the case $p = 0$, this integral is commonly called the ``Dirichlet Integral''.