Verified answer

u = x^2 + 3x + 4

du = (2x + 3) * dx

(2x + 3) * dx / (x^2 + 3x + 4) =>

du / u

Integrate

ln|u| + C =>

ln|x^2 + 3x + 4| + C

From 0 to infinity

ln|inf| - ln|4| =>

inf