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# Evaluate the integral.$\displaystyle \int \frac{dx}{\cos x - 1}$

## $$\int \frac{d x}{\cos x-1}=\csc x+\cot x+c$$

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

here we have the integral of one over co sign of X minus one. One way to proceed here is to multiply. That happened the bottom by one plus co sign X. So, after doing so, let's go ahead and multiply out the denominator with co sign X plus one in the numerator and in the denominator, we have cosign squared X minus one. So using the Pythagorean identity, we can rewrite this denominator as negative science. Where and then let's go ahead and split up this into grand into two fractions. We have coastline, eggs, overnegative, sign square plus one over negative science where using our knowledge of trigonometry, we could go ahead and re write these. So for the first in our group, we have negative Cho attention of X time's cozy Kennebec and for the second integral, we have negative Kosi can square of x, d, d x and we we know from our table or from previous examples that evaluate each of these two. So this is cozy convicts and the integral of negative Kosi can squared is coast engine of X, plus our constancy. And that's our answer

JH

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp