Tuesday, October 28, 2014

Advanced Math Solutions – Integral Calculator, advanced trigonometric functions, Part II

In the previous post we covered integrals involving powers of sine and cosine, we now continue with integrals involving powers of secants and tangent of the form \tan^n(x)\sec^m(x).

The general rule to evaluate \int \tan^n\left(x\right)\sec^m\left(x\right)dx is as follows:

  • If m is even and positive, take \sec^2(x) out, use the identity \sec^2(x)=1+\tan^2(x) to convert remaining sec to tan, and substitute u=\tan(x)
  • If n is odd and positive, take \tan(x)\sec(x) out, use the identity \tan^2(x)=\sec^2(x)-1 to convert remaining tan to sec, and substitute u=\sec(x)
  • If n is odd or even but there is no \sec(x) factor, use the identity \tan^2(x)=\sec^2(x)-1 and repeat the steps above
  • If none of the cases apply, try converting to sine and cosine

Let’s see how it works starting with an example where m is even (click here):

Simply combine the solutions and substitute back u=\tan(x).

Here’s another example where n is odd (click here):

One more example where n is odd with no factor of sec(x) (click here):

In the next post we’ll cover trigonometric substitution, stay tuned.



  1. Thanks for sharing.I found a lot of interesting information here. A really good post, very thankful and hopeful that you will write many more posts like this one.

  2. I recommend that you also read this blog article for some info on how to write amazing research paper using some tips. Good luck mate

  3. Awesome blog. I would love to see true life prepared to walk, so please share more informative updates. Great work keeps it up.
    700-551 exam questions

  4. Thanks you guys !! really helpful .such great work. Chase Bank Login

  5. KFC Customer Satisfaction Survey. We value your candid comments and respect you taking the time to finish our survey. kfc customer survey

  6. HealthFusion Login - Are you getting trouble while log into your account, No issue, Here is the complete step by step technique. Healthfusion Login

  7. TuTuApp is just an amazing app store from where you can download everything for free. TuTuApp is available for Android and iOS devices. TuTuApp

  8. If you are looking for the complete procedure of MyAARPMedicare Login guide and rewards, forgot the password, contact details, Plans, phone numbers and other things. www myaarpmedicare com