Question Detail

To evaluate this integral, we first complete the square in the denominator.Denominator: x2 + 4x + 7To complete the square for x2 + 4x, take half of the coefficient of x (which is 4/2 = 2) and square it (22 = 4).x2 + 4x + 7 = (x2 + 4x + 4) - 4 + 7= (x+2)2 + 3So the integral becomes:∫ dx / ((x+2)2 + 3)This is in the form ∫ du / (u2 + a2), where u = x+2 and a = √3.The integral formula is (1/a) tan-1(u/a) + C.Substitute u = x+2 and a = √3:(1/√3) tan-1((x+2)/√3) + CTherefore, the correct option is B.