integral of sqrt(tan(x)) by brute force

This is how you integrate sqrt(tan(x))! This is a pretty challenging integral!

[blackpenredpen]

Sorry for the reupload.

I actually had a mistake on the integral of 1/(x^2-a^2) in the previous video.

I will make up to you guys by checking my answer by differentiation! That video will be done soon!

[barqueros]

you know something is hard when blackpenredpen uses five colours

[Gillespie]

I think my professor summed up integration in a nice way. He said differentiation is all about technique. You see a scenario and have a set of rules you then follow. Integration is a form of art. It's much more intricate and delicate.

[MrSnowy]

Imagine doing all this and then forgetting the +c

[eganrabiee]

"Welcome to the Salty Spitoon, how tough are ya?"
"How tough am I? I just integrated a trig function!"
"Yeah, so?"
"integral(sqrt(tan x))dx"
"Uh, right this way..."

[whiz]

"1+1 is 2, right?"
Calculus, everybody.

[rileywells]

Mr Math Man.
Math Me a Man.
Make him integrate the square root of tan.

[Chrisuan]

Me when finding this channel: "wtf is going on?!"

Me rewatching 1 year later after having seen every bprp video: "alright easy didn't even need the DI setup"

[tesfayebabore]

this is pure game. There are very very few maths teachers at level of you. Thank you.

[vishsri]

Wow..you demonstrated this before 100k subs more than 3 years ago, today you have 687k. Wishing you for the next 313k

[XTheDentist]

I passed my semester of Calc 1! I did not fully understand everything but I believe I got a strong majority of it & I will be working on some of my weaknesses during break to prepare for Calc 2. For some reason when we got to U-substitution, everyone was confused but it seemed to make sense to me just based off the few example she gave in class and somehow that was all I needed. Anyway, so during last class before our final, she did a little review & answered questions. Someone asked about this sqrt(tanx) and she was like "oh you cant solve this with your current toolset, wait till next semester" and I was like "I can solve it" because I had all this false confidence from having understood the whole U-sub stuff. Well turns out this is a VERY difficult one lol. I guess if you are a student and want to be prepared for integrals, just spend a week studying just THIS one integral and you should be good to go lol.

[Shome]

I just saw you instagram reel, where you give credit question and searched for this integral on YouTube.
And I am so glad I found your video 😀!

[viktorsundstrom]

Integration is just the easiest thing ever... I can integrate √tanx + e^x² in seconds:

Set up the integral:
∫ √(tan(x)) + e^x² dt

And then just use the "inverse" power rule:

(t)√(tan(x))+ (t)e^x²

And we're done...


I didn't say that I'ld do it with respect to x...

[프로틴요플레]

I'm preparing a transfer exam for Korean universities and there was this question on my preparation problem set. Your solution was so helpful brother, thanks a lot!

[RyanLucroy]

14:41
"This is the two, so what should I do?" What a rhyme :O

[DGCubes]

Oh man, I love this video. I watched the entire thing and enjoyed every second of it! Keep up the good work on your channel. :)

[vidaroni]

You, my good sir, are turning calculus into art! Awesome video!

[FingertipsOfTheNight]

Ok, so in the beginning we have a pretty simple mathematical expression while the result in the end is something horrible. Things tend to evolve naturally from more complex to simpler. I therefore consider it normal to leave this formula unintegrated. Thank you for all your thumbs up ! :D

[rajendramisir]

I like this integral and its anti-derivative. I am impressed with your technique of using trigonometric and u-substitution along with algebraic manipulation to arrive at the answer.

[anthonyjaas]

Very well work dude, the resolution was easier than I thought, I had problems when using trinomio. You got a like and a new subscriber!