∫[0,√3a] 1/(a^2+x^2)
=∫[0,√3a] 1/a^2(1+(x/a)^2)
=1/a^2*∫[0,√3a]1/(1+(x/a)^2)
=1/a^2*arctanx/a|[0,√3a]
=1/a^2*π/3
=π/3a^2