Let $$I_n=\int_{-1}^1(1-x^2)^ndx.$$Use integration by parts to derive a recursion relation for the integral. After I used integration by parts the answer I got was $$\left.x(1-x^2)^n\rule{0mm}{6mm}\right|_{-1}^1+2n\int_{-1}^1x^2(1-x^2)^ndx$$ After this though I don't understand what to do next.
2026-03-30 05:10:11.1774847411
Derive a recursion formula for integral
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Hint: $x^2(1-x^2)^n=(1-x^2)^n-(1-x^2)^{n+1}$.