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

int sqrt(a^(2)-x^(2))

int sqrt((x+2)^(2)+2)dx

int sqrt((x+2)^(2)+2) dx

int sqrt((1-n)/(1+n))dn

If n is a positive integer and u_(n)=int x^(n)sqrt(a^(2)-x^(2))dx

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(sqrt(1+x^(2))-x)^(n)dx

(i) int sqrt(a^2-x^2) dx=____ (ii) int sqrt(x^2-a^2) dx= _____ (iii) int sqrt(a^2+x^2) dx=____

lim_(n rarr oo)(1)/(n^(3))(sqrt(n^(2)+1)+2sqrt(n^(2)+2^(2))+(-n)/(n sqrt((n^(2)+n^(2))))=

lim_(n rarr oo)(1)/(n^(3))(sqrt(n^(2)+1)+2sqrt(n^(2)+2^(2))+...+n sqrt(n^(2)+n^(2))) is equal to