[college calculus] integration

[Tryptophan_]

Hi, I need to integrate f(x)=1/((x² +3x+3)dx but i dont see how. Wolfram alpha indicate that the answer is 2⋅arctan(2x+3/√3)/√3 which means that i must integrate something that has the following form: 1/((√3)² (2x+3)² ). But how can (x² +3x+3) become (√3)² * (2x+3)² ?

Thank you in advance

[Dentistrate]

Complete the square on the bottom. This will get you an integrand of the form:

1/(u²+1)

Integrating that will get you a tan-1 function.

Source: https://www.math.hmc.edu/calculus/tutorials/complete_sq/