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)

2nd one sounds incorrect. x^2 + x^-2 > x^2 for all real non-zero x, and integral(0,infinity) e^(x^2/4) = +inf. Ergo integral(0,infinity) e^((x^2 + x^-2)/4) = +inf.

For the first, use arctan(a) + arctan(b) = arctan((a+b)/(1-ab)).