lol math competition

Okay, can't do these two.

Prove sum(k=1,n){arctan(1/(1+k+k^2))} = arctan(n/(n+2))

Show integral(0,infinity) e^{(x^2 + x^-2)/4} = sqrt(pi/e)

>>5
Yes. Yes, it does. And I'm too tired to dick around with it. :-/