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!

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[bprpcalculusbasics]

Watch next: What integration technique do we use?

[rogersmith-hf]

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

[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 Through the hyperbolic goniometric definitions you get the very same result. Thank for the video.

[fixtir]

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.

[mathunt]

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

[nostalgiez]

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

[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

[maakunanashi]

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

[wuyqrbt]

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

[Shahan]

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

[charalabosspyrou]

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

[haider]

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

[ahmedwahid]

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

[Shahan]

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

[izza]

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

[umamaheshwari]

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

[wuyqrbt]

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