Consider the integrals $I=\int \frac{\sin x}{3\cos x+4\sin x}dx$ and $J=\int \frac{\cos x}{3\cos x+4\sin x}dx.$ Then, the integral $4J-3I$ is equal to (where, $c$ is the constant of integration)

• A

  $\ln \left|3\cos x-4\sin x\right|+c$
• Correct answer
  B

  $\ln \left|3\cos x+4\sin x\right|+c$
• C

  $\ln \left|3\sin x+4\cos x\right|+c$
• D

  $\ln \left|3\sin x-4\cos x\right|+c$

Hence, the correct answer is option: 'B'.