Integral of sqrt(x^2+1), integral of sqrt(x^2-1), integral of sqrt(1-x^2)

In this calculus tutorial, we will do the classic trigonometric substitution problems, namely, integral of sqrt(x^2+1), integral of sqrt(x^2-1), integral of sqrt(1-x^2). These are some must-know examples for your calculus 2 class! Best wishes to you in your class!
Calculus 2 Integration techniques: • Integral Techniques, C...
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[@bprpcalculusbasics]

Watch next: What integration technique do we use?
ruclips.net/video/HiXfAayQ_8o/видео.html

[@fixtir947]

thanks, man I seen a lot of videos and I liked how you explained how to come back to the x world the best. I was very confused.

[@user-bt4vm3jl2j]

Gracias hermano me resolviste el examen eres un artista de las matemáticas.

[@Ragnak_]

How do I easily remember all the formulas and identities? They're so many to remember, idk if I can keep track of them all

[@mathunt1130]

I'd be tempted to do a hyperbolic sub in the first integral. It comes out easier.

[@akashbhatti5141]

Thank you sir

[@ChrisRossaroDidatticaDigitale]

In the first one I'd use this substitution: x=ch(t); in this way, by using ch^2(t)-sh^2(t)=1 and dx=sh(t)dt, one gets int{sh^2(t)dt}; thus, integrating by part =1/2*{sh[settsh(ch(x))]-settch(x)}+c. Through the hyperbolic goniometric definitions you get the very same result. Thank for the video.

[@jackkalver4644]

Same for the second.

[@user-wu8yq1rb9t]

I have a recommendation (or request).
Please make a video about the *Wallis Product*.
Thank you

[@nostalgiez3429]

Fastest way to do integals like that is by integration by parts just let initital function to be u ( u = sqrt(x^2 + 1)) for example, you will get answer pretty quick

[@ocethanol]

i'm one year late, but can you teach me about this method?
i just need a solution for your example, that would be great

[@ahmedwahid8421]

is the sec function always positive, you must write the absolute value... of sec

[@charalabosspyrou5057]

On the second integral shouldn't root tanθ²= |tanθ|??

[@izza2319]

This helps so much, thank youuu! And also the pokemon ball, so cute😆

[@Shahan1980]

I can't remember even one problem from higher schoo; or university where we used sec or cosec? I mean I know what it is, but didn't even write the formulas involving those two. sin and cos was always enough? though, ok, fractions might appear, but, from the other point of view trig functions are all about fractions, just meticulously hidden

[@maakunanashi4508]

May i know if you have vid all manual integrals of those? Coz i think its much easier to know that than memorizing them directly

[@maakunanashi4508]

Like what you did in 14:08

[@haider1946]

Question: can I return to the x world while integrating?

[@roger12321]

No

[@haider1946]

@@roger12321 dang

[@anshumanagrawal346]

Yes, you can

[@Shahan1980]

that's funny how hypotenuse ended up a hypanious (as far as I can hear) LOL

[@PriyankaKumari-jn6ej]

♥️♥️♥️♥️

[@umamaheshwari8877]

Easily we can do this by using a formula of integration of square root of x2 + a2 no need to do this process

[@xihadimran1600]

Why x=sin theta😰😰??

[@user-wu8yq1rb9t]

But I prefer to stay in Disney world then Resorts world !

[@bprpcalculusbasics]

lol

[@MathAdam]

First!

[@youngmathematician9154]

Second!

[@mathevengers1131]

Third!

[@pravargupta6285]

@@mathevengers1131 Fourth!

[@anshumanagrawal346]

lol

[@user-wu8yq1rb9t]

Fifth!