Solution
= Solution
Apply the <power-complement integral recurrence> three times, starting from $I_{0,1}(\pi/2,0)=1$:
$$
\boxed{I_{3,1}(\pi/2,0)=\frac9{10}\frac67\frac34=\frac{81}{140}}.
$$
Each factor corresponds to reducing $n$ by one; the final unreduced <integral> is just $\int_0^{\pi/2}\cos u\,du=1$.