Question Detail

To evaluate this integral, we need to complete the square in the denominator.x2+4x+7 = (x2+4x+4) + 3 = (x+2)2 + 3.So the integral becomes ∫ dx/((x+2)2 + 3).This is in the form of ∫ du/(u2 + a2) = (1/a)tan-1(u/a) + C.Here, u = x+2, so du = dx.And a2 = 3, so a = √3.Substituting these values into the formula:= (1/√3)tan-1((x+2)/√3) + C.This matches option B. (Note: The source document indicates option A was selected, but based on the calculation, option B is correct).