∫(2,0) 1/(4+x²) dx
=∫(2,0) (1/4)/(1+x²/4) dx
=∫(2,0) (1/2)arctan(x/2) dx
=(1/2)arctan(x/2)|(2,0)
=π/8
arctan'(x) = 1/(1+x²)
arctan(x/2) = (1/2)/(1+(x²/4)) =2/(1+x²)