Integral of 1/(t^2*sqrt(t^2-16)), trig sub, know this for your calculus 2 class

Integral of 1/(t^2*sqrt(t^2-16)), trig substitution, calculus 2 tutorial.
----------------------------------------
#blackpenredpen #math #calculus #apcalculus

[quahntasy]

I press Like first then I start watching.
0 dislikes as of yet. He is probably the best math tutor YouTube has to offer.

[tamircohen]

Haven't started calculus class yet but got this correct from your videos in the past. Thanks!

[holyshit]

In fact there are two substitutions to avoid trig sub
1. Integration of binomial differentials
2. Euler substitution a>0 case
In this integral we can also calculate it by parts
Before parts we just need to rationalize the integrand

[wristdisabledwriter]

I burst out laughing when I realized it was the integral of cos

[mayerlyjulissaquinonesquin]

Soy colombiana y aunque no entiendo el idioma este ejercicio es el mismo que me toca resolver asi que Thanks🌸

[marcioamaral]

I don't know why but I love trig sub

Even if the integral is easy as this one I always love to see a sin or a cos

[xenngaming]

Thank u sir, I also find this question in my study stuff, and I think I should use "algebraic twin's"
Thanks for teaching us,

Can u make a video on examples of LEIBNITZ's RULE

[victor]

I remarqued that the recent videos on this channel seem a bit more detailed and overly easier to understand than the other, older videos

[paulraj]

i like this one better. but hw do you know we must go for sec teta substitution? by few trials of solving? hw to get an immediate idea to solve bizarre kind of integration problem.

[herodevlin]

Another Method(without using trigo substitution)

Let u=1/t, dt=-1/u^2du
(-1/u^2)]du
=inte[-u/sqrt(1-16u^2)]du
=1/16 sqrt(1-16u^2)+C
=1/16t sqrt(t^2-16)+C

[RAG]

you could have just used t=4cosU. Very straightforward.

[leonardnecula]

I let t = 1/u, du = -1/(t^2)dt, after the substitution we are left with - u/sqrt(16u^2 -1 )du in the integral . We notice that u = 1/32(16u^1 - 1) ' so the integral it's the same as integral of -(1/32) * 1/sqrt(x) dx = - (1/16 )* sqrt(x) with x = 16u^2 - 1 so the integral in the u world it's - (1/16) * sqrt ( 16u^2 - 1 ). If we get back to the t world we have -1/16 * sqrt | 16/t^2 - 1 | = -1/16 *sqrt |16 - t^2 | / | t | .

[Nithesh]

multiplying the top and bottom by t^-3, then t^-3/sqrt(16-t^-2) can be integrated by a simple u sub...

[رأفتالهاشمي-قم]

hope you can help me in this integration dt/t-√(1-t^2) 😔😔😔

[ErInfo-jgtt]

Plz sir solve lot of problems. I need. Make a long video

[nlain]

3:31 which identity does this come from?

[jamesa.]

Wouldn't partial fraction decomposition be easier

[abhinavsharma-gymi]

Take t^2 common from square root and then take simplified square root as x for substitution.This is easy too.

[anjelpatel]

I saw the problem and tried with u sub, got answer...Tapped the play button...heard you sayin "Here, u sub won't

[QuippersUnited]

You don't have the built up hostility that many of my professors did: a lot of them would have violently thrown the spent blue pen.