int_(0)^(oo)(dx)/((x+sqrt(x^(2)+1))^(3))=

int_(0)^(1)(dx)/((x+sqrt(x^(2)+1))^(3))=

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

If n>1, then int_(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n)) equals

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

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

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

int_(0)^(oo) (x)/((1+x)(1+x^(2)))dx=

int_(0)^(oo)(1)/(x+a)dx

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta