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int0^oo(dx)/((1+x)sqrt(x))...

`int_0^oo(dx)/((1+x)sqrt(x))`

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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)/((x+sqrt(x^(2)+1))^(3))=

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

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

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

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