Question

Given the integral of (1/(1+9x^2)dx taking u =3x.
Use integration by substitution

Answer 1

u = 3x
du = 3dx => dx = 1/3 du
Integral of (1 / (1 + 9x^2))dx = 1/3 (integral (1/(1 + u^2))du) = 1/3 arctan(u) + c = 1/3 arctan (3x) + c