| I[n]=∫[-1,1](1-x^2)^ndx=[x(1-x^2)^n][-1,1] - ∫[-1,1]x*n(1-x^2)^(n-1)(-2x)dx =2n ∫[-1,1]x^2(1-x^2)^(n-1)dx =-2n ∫[-1,1](1-x^2)(1-x^2)^(n-1)dx+2n ∫[-1,1](1-x^2)^(n-1)dx =-2nI[n]+2nI[n-1] I[n]={2n/(2n+1)}I[n-1] I[1]=∫[-1,1](1-x^2)dx=4/3 ∫[-1,1](1-x^2)^5dx=I[5]=(10/11)*(8/9)*(6/7)*(4/5)*I[1] =(2/11)*(8/3)*(2/7)*(4)*(4/3)=512/693
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