Integral of sec(x) but without that trick!

Integral of csc(x) without that trick

[pbj]

Ah this "mechanical" evaluation is much better than the "magical" original because this shows all the relevant motivation and isn't too hard either!

[pablorestrepodiaz]

wow u love this video, its like magic when you demostrate that those 2 expression are the same

[itszeen]

Love it when there is a new upload when I get home from school!

[ishaanivaturi]

This is so nice! I was curious about the same thing last year and ran through this same derivation too! Glad to know you're bringing it to everyone :)

[changenow]

100 differential equations please...thank you

[JohnSmith-rftx]

CHEATER!!! :)

You claimed you would do the integration without using the the trick of multiplying by (sec x + tan x)/(sec x + tan x) but that's exactly what you did in the process of converting your answer to the standard form. You may have dressed it up in different clothes, but it's still there! At 2:34, you first multiply by (cos x)/(cos x). Well, that's the same as multiplying top and bottom by (1/cos x). Then, at 8:20, you use (1 + sin x)/(1 + sin x). When you multiply those two together, you get exactly the (sec x + tan x)/(sec x + tan x) you claimed you wouldn't use.

[VibingMath]

Thanks man! This technique is also applicable to integrate cosec x and it's more natural to do in this way rather than multiplying a complicated expression in the first place! I will let my students to watch this so they dont need to memorize that trick! Yay!

[MrAznBoyWins]

you have a real heart of a teacher, love to see it

[Nonsense_]

I'm in my first calculus class, and just today I was wondering how to integrate that thing. Coincidence or destiny?
Great vid as always. Greetings from Honduras :D

[japotillor]

A way for me to remember it Is that one multiplies top and bottom by 1 which is (sec x)^2 - (tan x)^2, which factors to (sec x + tan x) (sec x - tan x) Eliminating the (sec x - tan x) terms, you get sec x + tan x :)

[GreenMeansGOF]

I think it all comes down to already knowing the answer. The second way is more intuitive but the first way is faster.

[maliciousmarka]

Great explanation on this video! Thanks for helping me understand :)

[ieqvilamaria]

Bprp Thanks for yours videos, them are awesome so much, I am your fan!! :)

[jeffreys]

im new to this channel and i love how he smiles after doing a step like that shows how he loves maths😀 and boys girls find these kind of boys attractive bcz they like the men with dedication (kinda motivation for the boys)😂

[yashovardhandubey]

This was uploaded at 3 am in the morning in my Still watched it

[krukowstudios]

Nice one. I think it is a bit sad that we do not really see cosecant and cotangent that often. I would love to see more of them :D

[thomasarch]

Actually once you get the integral into the form of ((cos x ) / ( 1 - (sin x)^2 ) ) dx you are done as the answer is artanh (sin x) + C! Just use the hyperbolic tangent function. Finshed!!
No fooling around with partial fractions.

[eduth]

I love this video!!! I always hated that trick!

[dr.rahulgupta]

Excellent presentation ! 👌 black pen - red pen -green pen.

[Peter_]

blackpenredpen is one of the most likeable guys I know of on YouTube.