What Is The Integral Of 1/Sec^2X, Integrate 1/Sec^2(X)

I got $\ln|\sec(2x +1) + \tan(2x+1)| + \text C$ as an answer. I saw that the integral of $\sec x$ is $\ln|\sec x + \tan x| + \text C$. But I feel I may have left something out because that was too easy.

You are watching: Integral of 1/sec^2x

Set $2x+1=u\implies 2dx=du$

$$\int\sec(2x+1)\ dx=\frac12\int\sec u\ du=\frac\ln2+K$$

Replace back $u$ with $2x+1$

Let $u=2x+1$. Then $\text du=2$$$\int \sec(2x+1) \ \text dx=\int \frac\sec(u)2 \ \text du$$$$=\frac 12\int \sec(u) \, \text du$$$$=\frac 12\ln|\sec(u)+\tan(u)|+\text C$$Reverse the substitution$$\frac 12\ln|\sec(2x+1)+\tan(2x+1)|+\text C$$$$\colorgreen+\text C$$

Thanks for contributing an answer to hyakkendana-hashigozake.comematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up with references or personal experience.

Use hyakkendana-hashigozake.comJax to format equations. hyakkendana-hashigozake.comJax reference.

See more: Where"S Runnicles: The Chances Of Anything Coming From Mars Are A Million To One

To learn more, see our tips on writing great answers.

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged calculus integration or ask your own question.

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.

17/09/2021

Integral of 1/sec^2x

Not the answer you're looking for? Browse other questions tagged calculus integration or ask your own question.