`I=int(n^2dn)/(sqrt(a^(3)-n^(3)))`

int sqrt(a^(2)-n^(2))dn

int(n)/(sqrt(n-3))dn

If I_(n)=int x^(n)sqrt(a^(2)-x^(2))dx, prove that I_(n)=-(x^(n-1)(a^(2)-x^(2))^((3)/(2)))/((n+2))+((n+1))/((n+2))a^(2)I_(n-2)

int(1)/(sqrt(8+3x-n^(2)))dx

If I_(n)=int(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

Let I_(n)=int(x^(n))/(sqrt(x^(2)+2x+5))dx then I_(n)=(x^(m-1))/(n)sqrt(x^(2)+2x+5)-lambda I_(n-1)-mu I_(n-2) where lambda,mu and m' are involving n' then

lim_(n rarr oo)(sqrt(n^(3)-2n^(2)+1)+3sqrt(n^(4)+1)3)/(4sqrt(n^(6)+6n^(5) )+2)-5sqrt(n^(7)+3n^(3)+1))

I=int(sinn)/((1-cos n)^(2))dn

int(n^(4))/((n-1)(n^(2)+1))dn

Evaluate : lim_(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2)(3sqrt(2)+4sqrt(n))^(2))+(sqrt(n))/(sqrt(3)(3sqrt(3)+4sqrt(n))^(2))+.......+(1)/(49n)]