(1)/(x^(n)+a^(n))*(1)/(sqrt(x+a))

The value of the integral int_((1)/(n))^((an-1)/(n))(sqrt(x)dx)/(sqrt(a)-x+sqrt(x)) is -

(x^(n-1))/(sqrt(1+4x^(n)))

If y= {x + sqrt(x^(2) + a^(2))}^(n) prove that (dy)/(dx)= (ny)/(sqrt(x^(2) + a^(2))). n gt 1 ne N

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)

(1)/(sqrt(4x+1)){((1+sqrt(sqrt(x+1)))/(2))^(n)-((1-sqrt(4x+1))/(2))^(n)}=a_(0)+a_(1)x

The value of int_(1//n)^((an-1)//n) (sqrt(x))/(sqrt(a-x+sqrtx))dx , is

The value of int_(1//n)^((an-1)//n) (sqrt(x))/(sqrt(a-x)+sqrtx)dx , is

int_(1/n)^((an-1)/n) sqrt(x)/(sqrt(a-x)+sqrt(x))dx= (A) a/2 (B) (na+2)/(2n) (C) (na-2)/(2n) (D) none of these

int_(1/n)^((an-1)/n) sqrt(x)/(sqrt(a-x)+sqrt(x))dx= (A) a/2 (B) (na+2)/(2n) (C) (na-2)/(2n) (D) none of these