In the previous post we covered common integrals (

click here). There are a few more integrals worth mentioning before we continue with integration by parts; integrals involving inverse & hyperbolic trig functions. We kept these for later, as they are usually used with substitution.

- \int \frac{1}{x^2+1}dx=\arctan \left(x\right)+C
- \int \frac{1}{\sqrt{1-x^2}}dx=\arcsin \left(x\right)+C
- \int \frac{1}{1-x^2}dx=\arctanh \left(x\right)+C
- \int \frac{1}{\sqrt{1+x^2}}dx=\arcsinh \left(x\right)+C

Let’s take a look at a few examples, notice that we are trying to manipulate the functions to a known form (can be tricky)

Here’s an example using algebraic manipulation and substitution (

click here):

Here’s another example using substitution to get to the common form (

click here):

Here’s another example using substitution to get to the common form (

click here):

Ready for integration by parts!

Cheers,

Michal

Thank you very much for sharing this article with us, guys! You are doing a great thing!

ReplyDeleteAnd you're doing a terrible thing with that useless link.

ReplyDeleteThank you very much for sharing this article with us, guys! You are doing a great thing!

ReplyDeletequickpayportal

wow good article with nice info thanks you Quickpayportal

ReplyDeleteHelpful article for students.

ReplyDeleteWebsite Design Company

If you're looking for a decent paper writing service, you should definitely pay attention to this article: https://justbuyessay.com/blog/online-essay-writing-services

ReplyDeletensects and rodents known and spread, such as cockroaches and home termites as well as mice, mites, termites and other insects that cause inconvenience As well as make the environment of the house unhealthy and uncleanارخص شركة مكافحة حشرات

ReplyDelete