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This integral is of the form ∫du/(a² + u²) = 1/a tan⁻¹(u/a) + C.First, identify a² and u² in the denominator 4 + 9x²:a² = 4 => a = 2u² = 9x² => u = 3xNext, find du from u = 3x:du = 3 dx => dx = 1/3 duSubstitute these into the integral:∫dx/(4+9x²) = ∫(1/3)du/(2² + u²)= 1/3 ∫du/(2² + u²)Now apply the integral formula:= 1/3 * 1/2 tan⁻¹(u/2) + C= 1/6 tan⁻¹(3x/2) + C. This matches option B.