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
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.
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
Watch next: What integration technique do we use?
ua-cam.com/video/HiXfAayQ_8o/v-deo.html
Gracias hermano me resolviste el examen eres un artista de las matemáticas.
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.
I'd be tempted to do a hyperbolic sub in the first integral. It comes out easier.
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
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
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.
Same for the second.
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
I have a recommendation (or request).
Please make a video about the *Wallis Product*.
Thank you
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
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
Like what you did in 14:08
Thank you sir
Question: can I return to the x world while integrating?
No
@@roger12321 dang
Yes, you can
On the second integral shouldn't root tanθ²= |tanθ|??
is the sec function always positive, you must write the absolute value... of sec
This helps so much, thank youuu! And also the pokemon ball, so cute😆
that's funny how hypotenuse ended up a hypanious (as far as I can hear) LOL
Easily we can do this by using a formula of integration of square root of x2 + a2 no need to do this process
But I prefer to stay in Disney world then Resorts world !
lol
Why x=sin theta😰😰??
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@@mathevengers1131 Fourth!
lol
Fifth!