Recurrence relation for integral Find a recursive relation for the integral $\int(1-x^2)^\frac{n}{2}$ :
Pretty sure partial integration is the way to go since we haven't learned anything past that. My try:
The only non-tedious way to split this for a partial integration is 
$u=(1-x^2)^\frac{n}{2}$  $dx=dv$
$du=-nx(1-x^2)^{\frac{n}{2}-1}$ $x=v$
$\int(1-x^2)^\frac{n}{2} = x(1-x^2)^\frac{n}{2} + n\int x^2(1-x^2)^{\frac{n}{2}-1}$
Not quite a recurrence relation yet. I tried partial again on the second integral but that didn't work too well. Any suggestions?

Write $n\int x^2(1-x^2)^{\frac{n}{2} -1}$ as $$-n\int(1-x^2)^{\frac{n}{2}}+n\int (1-x^2)^{\frac{n}{2}-1}=-nI_n+nI_{n-2}.$$
