Best solutions to - "Evalauate the following integral. ∫dxcos⁡x−1"

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Answered question

2021-10-24

Evalauate the following integral.

\int \frac{d x}{\cos x - 1}

Clara Reese

Skilled2021-10-25Added 120 answers

Step 1
Evaluate the integral:

\int \frac{d x}{\cos x - 1}

We have identity:

1 - \cos x = 2 \sin^{2} (\frac{x}{2})

Therefore,

\int \frac{d x}{\cos x - 1} = \int \frac{1}{- 2 \sin^{2} (\frac{x}{2})} d x

= \frac{1}{2} \int - \cos e x^{2} (\frac{x}{2}) d x

= \frac{1}{2} \cdot 2 \cot (\frac{x}{2}) + C

= \cot (\frac{x}{2}) + C

Step 2
Hence, required answer is

\cot (\frac{x}{2}) + C

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