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First, complete the square for the denominator: x2 + 4x + 7.x2 + 4x + 7 = (x2 + 4x + 4) + 3 = (x+2)2 + 3.The integral becomes: ∫ dx / ((x+2)2 + 3).This is in the form of the inverse tangent integral: ∫ du / (u2 + a2) = (1/a) arctan(u/a) + C.Here, u = x+2 (so du = dx) and a2 = 3, which means a = √3.Substitute these values:= (1/√3) arctan((x+2)/√3) + C.Note: arctan(x) is also written as tan-1(x).