What is the integral of (3x+1)/((x^2)+3)?

Answer 1

Hints:

1. Presumably, you know the integral of 1/(x^2+1). So you also know the integral of 1/(3y^2+3).

2. If z = x^2+3, dz = 2x.

3. So split the fraction into the sum of two pieces, and integrate each piece with the help of a change of variables.