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)

e^{(x^2 + x^-2)/4} -> e^{-(x^2 + x^-2)/4}
Mathematica yields right answer.

>>4
Does bullshit long answer involve erfs? lol