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" 34."int(0)^(oo)(dx)/([x+sqrt(x^(2)+1)]...

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

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

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

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

Show that int_(0)^(oo) (dx)/([x+sqrt(x^(2)+1)]^(3)) = (3)/(8)

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

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

int_(0)^(1)(dx)/(3sqrt(x))

int _(0)^(oo) (dx)/((x+ sqrt(x^(2)+1))^(3)) is equal to

If n gt 1 . Evaluate 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)