good day please help with this indefinite integral,especially what formula i can use to solve it-2x+1/(3x^2+3x+5)dx.Find the indefinite integral.

since there's a quadratic in the bottom, and a linear factor in the top, it's a good bet you can massage it into something like du/u.

In fact, if we let

u = 3x^2+3x+5
du = 6x+3 = 3(2x+1)

and you have
∫ 1/3 du/u = 1/3 log u + C
= 1/3 log(3x^2+3x+5) + C