Integral of csc(x) and sec(x)

Published December 9, 2008 How To , Integration , Mathematics 3 Comments
Tags: Integration, Mathematics, trigonometric-substitution, u-substitution

The integrals of sec(x) and csc(x) can usually be found in tables of integrals, and if all you are looking for is the answer, then here it is:

$\int \sec(x)dx = \ln \lvert \sec(x) + \tan(x) \rvert + C$

$\int \csc(x)dx = \ln \lvert \csc(x) + \cot(x) \rvert + C$

However, if you would like to know more, then here are the derivations for the integrals broken down step-by-step. I tried to give as much detail as possible so it would be easy to read and comprehend.

Proof for integral of sec(x).

Proof for integral of csc(x).

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3 Responses to “Integral of csc(x) and sec(x)”

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1 Jane March 6, 2009 at 8:40 PM

Thank you so much!
I was looking all over for the proofs, and you provided just what I need!

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2 hadush February 26, 2012 at 11:54 AM

i am so confused with that ansewer

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3 hadush February 26, 2012 at 11:55 AM

becouse there must be a negetive sign infront of the lan

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