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This integral is of the form ∫du / (a² + u²), which integrates to (1/a) tan⁻¹(u/a) + C.In the given integral ∫dx / (4+9x²):We have a² = 4, so a = 2.We have u² = 9x², so u = 3x.Then, the differential du = d/dx(3x) dx = 3 dx. Therefore, dx = du/3.Substitute these into the integral:∫(du/3) / (2² + u²) = (1/3) ∫du / (2² + u²)Now apply the formula:= (1/3) * (1/2) tan⁻¹(u/2) + C= (1/6) tan⁻¹(3x/2) + C.This matches option B.