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TS EAMCET · Maths · Indefinite Integration

\(\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=\)

  1. A \((\cos 2) x-\frac{1}{3}(\sin 2) \log |\sec (3 x+2)|+c\)
  2. B \((\sin 2) x-\frac{1}{3}(\cos 2) \log |\cos (3 x+2)|+c\)
  3. C \((\sin 2) x+\frac{1}{3}(\cos 2) \log |\cos (3 x+2)|+c\)
  4. D \((\cos 2) x+\frac{1}{3}(\sin 2) \log |\sec (3 x+2)|+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((\cos 2) x+\frac{1}{3}(\sin 2) \log |\sec (3 x+2)|+c\)

Step-by-step Solution

Detailed explanation

\(\int \frac{\left(1-4 \sin ^2 x\right) \cos \pi}{\cos (3 x+2)} d x=\int \frac{\left[1-4\left(1-\cos ^2 x\right)\right] \cos x}{\cos (3 \pi+2)} d x\)…