$\int \frac{1}{4 \cos ^3 x-3 \cos x} d x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int \frac{1}{4 \cos ^3 x-3 \cos x} d x$ is equal to :

Options:

$\frac{1}{3} \ln |\sec 3 x-\tan 3 x|+c$

$\frac{1}{3} \ln |\sec 3 x+\tan 3 x|+c$

$\frac{1}{4} \ln |\sec 3 x+\tan 3 x|+c$

$\frac{1}{4} \ln |\sec 3 x-\tan 3 x|+c$

Correct Answer:

$\frac{1}{3} \ln |\sec 3 x+\tan 3 x|+c$

Explanation:

Let I = $\int \frac{1}{4 \cos ^3 x-3 \cos x} d x=\int \frac{1}{\cos 3 x} d x$

$=\int \sec 3 x d x=\frac{1}{3} \ln |\sec 3 x+\tan 3 x|+c $

Hence (2) is the correct answer.