int(dx)/(x sqrt(x^(2n)-a^(2n)))

int(dx)/(xsqrt(x^(2n)-a^(2n)))

int(dx)/(x sqrt(a^(n)+x^(n)))

int(dx)/(x sqrt(a^(n)+x^(n)))

int(x^(n-1)dx)/( sqrt(a^(n)+x^(n)))

If n gt 1 . Evaluate int_(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

int_(0)^(oo)(dx)/([x+sqrt(1+x^(2))]^(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)

Show that int_(0)^(oo) (dx)/((x+sqrt(1+x^(2)))^(n))=(n)/(n^(2)-1), (n in N, n gt 1)