Use the standard formula ∫a2x2+b2dx=(x/2)a2x2+b2+(b2/(2a))log∣ax+a2x2+b2∣+C. With a=2,b2=9, the result is (x/2)4x2+9+(9/4)log∣2x+4x2+9∣+C. Option 1 most closely matches this structure.
Note: The log coefficient in option 1 is 9/2, while the textbook formula gives 9/4; we have picked option 1 as the closest intended answer.