Trig Substitution:
dx/((x^2+a^2)^(3/2). What should you use for the trig substitution.
x = a tanθ
x^2+a^2 = a^2 sec^2θ
dx/(x^2+a^2)^(3/2) = 1/a^3 cos^3θ
To integrate that, use cos^3θ = (1-sin^2θ) cosθ
and in three or four steps you should wind up with
x/(a^2 √(x^2+a^2)) + C