What Integration Technique Do I Use ? Example 2

[@SepiaDragoonGR]

This is legit the best horror movie i've ever watched. 10/10

[@ozzman1997]

Calculus: Where a solution can look more intimidating than the problem that you started with.

[@seanki98]

This deserves a standing ovation.

[@patrickjmt]

Clap clap

[@DeadMeme5441]

+patrickJMT lol Clap clap by us to thank YOU!

[@mattt1994]

Just finished the last university math exam I will ever write. Thanks for all your help Patrick and best of luck to anyone still writing finals!

[@BurritoBalladBBd]

Just wanted to mention that I had purchased the problems and they were extremely helpful for my Calc 2 skills. If you're struggling you should really consider it.

[@freshely9309]

This video single-handedly developed my understanding of integrals, calculus and trig substitution in one video and one equation! Thank you so much, I now know much more about the fundamentals.

[@Snoop_Doge]

if our prof bring a question similar to this in a final or midterm, i will dance naked in the uni

[@yootantonystark2738]

so did you dance?

[@syafiqadly9428]

You have video of it? xD

[@hamdimohammed2541]

No worries, I'll join you! :P

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Your problem solving abilities are freakishly inspiring

[@dpcon1994]

That is intense... fair play...

[@patrickjmt]

i found calc 3 harder personally.

[@feelingzhakkaas]

Absolutely wonderful

[@tiisetsojames6378]

Patrick you the man man

[@ريفانسعد-ع2ذ]

you can use trig sub from the beginning and get sec^2(theta) ln(sec theta) and then use IBP's ,by differentiate ln(sec theta) and integrate sec^2 theta . I integrated tan^2 theta by rewrite as sin^2 theta/coc^2 theta ,, actually rewrite as sec^2 theta - 1 is way easier

[@212ntruesdale]

Excellent! However, I integrated tan^2theta by rewriting as sec^2theta -1, making two well-known, easy integrals.

[@matthewmartel9295]

I hope this isn't one of the questions in my test tomorrow...

[@patrickjmt]

i use my head

[@dude157]

For problems this complicated, i use wolfram alpha

[@elbay2]

Patrick, this was very well explained, and was quite the example! The only thing missing was partial fractions! Well done!

[@willemjacobussnyder8596]

Dude without this channel I would definitively have failed math this year. You're a legend bruv.

[@gotmilk606]

What an epic journey this has been. I thank you.

[@jegoodarms1559]

I can understand him better than my own professor. Good job!!

[@messi3119]

first trigonometry.....after that hyperbola parabola ellipse and now...integrals!!! THANKS patrick :) before your tutorials maths for me a nightmare bt now i can easily solve all the problems....thanks once again

[@elizamlokozi9833]

thanks much for this program am a form six student having one month holiday but am able to study integration without a text book ,more integration questions please

[@alaaashraf8472]

thank you very much it is very helpful. i am a student in cairo university of engineering and i love your videos thank you

[@jongeetard1259]

@E.AmmarAmmar Switch the limits around, let s=0, you get -(-2 to s) 1/x dx, integrate, -ln |x|, insert the limits, use the logarithm rules to get ln |-2/s|,then ln(2/|s|) and evaluate the limit as s->0, which is infinity if I remember right. I think that's how you would do it. Please correct me if I'm totally wrong.

[@omaralanis9436]

I solved the problem myself before you showed your method, and I got the same answer doing trig-sub first and then IBP. Will that always work or was this just a lucky example? I got ∫[sec^2θ*ln(secθ)]dθ after my first step...

[@ShyamSundarjps]

You can use this rule to get u and dv... and its called [ILATE] - (inverse trigonometric, logarithmic, algebraic, trigonometric, and exponential) arrange the given integral in this order to get u and dv easily. u will be the first term and dv will be the second... :D

[@stupid2574]

I learned to switch the I and L so LIATE. Do you know which is the correct way?

[@northernskies86]

It's LIATE (you will see it spelled out this way in every calculus textbook.)

[@AnthonyMoody]

1:22 I think you can start off with a trig substitution letting x = sec(theta) then using by parts after you get to sec^2(thet) * ln(sec(thet)). I got the same answer in the end so ..unless I made a convenient error 😂(which is definitely possible)

[@willieklein6707]

An absolute beast of problem!

[@Hunar1997]

if this was an exam i prefer leaving it and don't care about the marks

[@nonyvip1]

I love your videos so much

[@Survive2ToThrive]

more more more examples like this please, loved it!

[@Engineer1T6]

im pretty sure that Calc 2 covers all of integration, serieses, polar coordinates, vector valued functions calc 3 is surface integrals multiple integrals stokes theorem, greens theorem, partial derivatives

[@majrohi1]

Hey Patrick, Can we us the integration of (tan^2 X) as = ln(sec^2 X)+C.. Coz I know the integration of a tanX is indeed equal to ln(secX)+C. but not sure about that square of tangent.

[@swagconundrum]

You are an amazing human being

[@georgesadler7830]

Thank you for the video.

[@LifttheDead30]

You could have used trig substitution right from the beginning, turned it into a basic integration by parts problem with u=lnsecx and v = integral of sec^2x.

[@obo190]

unffff

[@codylaw7739]

yes but then the ride wouldn't be as fun lol

[@PARAMETATRONIC]

Maany thanks Patrick! You are the WD40 of rusted brains :) Btw since tan is an odd function souldn't we consider the sign of x such that tan(theta) = (x/|x|) . sqrt(x²-1) ?

[@cjohn41]

Jeez big pat... that was impressive

[@alexandretaranoff714]

Just wondering why is dx = sec teta tan teta dx. Because i thought the derivate of sec teta = -1/ square root of 1-teta^2 right ?

[@xiii1818]

Is this the only solution? it should be there's another way of the steps? Am I wrong?

[@rajanpoli4066]

how u know u have to take x=sec theta ..i took x=sin theta .. and it was a complicated answer . could you help me ?

[@joe27941]

I'm pretty sure you can actually instead start out with a trig sub, and then do integration by parts. That's what i did and ended up with the same answer

[@russiachan2]

Just so you know, you can also use trig substitution at the very beginning and get the same answer.

[@SoleSoulSeoul]

Integration is absolutely ridiculous

[@northernskies86]

Differentiation was a piece o' cake for me. Integration was the most confusing crap on the other hand.

[@mariahslittlelamb8049]

@@northernskies86 It is easy af

[@thewatcherlollol]

@@mariahslittlelamb8049 Shut up

[@dontbugmefool]

What type of pen is that? Looks nice :3

[@hamdimohammed2541]

Integration is pretty weird and unpredictable, how on earth did arcsec end up in the solution? :| Also, is that the only solution?? Is the antiderivative unique? please reply, I wanna know

[@cowpacino]

this is off topic, but I love that rollerball pen, I have one just like it

[@broa948]

You mean: if u don't know how to use trig identities... Just sit down and cry! hahaha

[@mariahslittlelamb8049]

idiot

[@nubsmacker]

For now I'm just a broke student, however, massive donation coming your way once I graduated! :)

[@cdubbz11188]

Any input on difficult wronskian diff Eq's?

[@malishmodestopeter6017]

I have got points , thanks but what does this statement mean "give three examples for Application of Integration"

[@inertia9325]

malish modesto Peter it means write down some places where you might use integration to solve something. For example, finding the area under a curve is an application of integration.

[@gene546]

man you're great, thanks for the videos.

[@carolinemitchell5711]

The nightmare is over. Fantastic!

[@mattt1994]

Good luck!

[@edderiofer]

I saw the bottom part of the fraction and immediately thought "Aha! It's an arcosh integral!"... ...When I tried, I ended up having to work out the integral of x/SQRT((x^2)-1) anyway. Trust me to have overthought the problem.

[@SNLshooter]

What college did you attend?

[@matthewk5827]

Why couldn't you do trig sub for the first problem. x^2-a^2

[@hamamath7195]

thx man you are very good i love math for ever

[@shiRo484]

YOU"RE THE BEST!

[@lanolinetoring6097]

Oh my god!!! Youre so good.! Thanks for the help man :)

[@patrickjmt]

you are most welcome!

[@thatoneguy257]

how did you know to use sec for the U sub

[@jamesmoriaty1098]

I'm only 3 yrs old n totally get this .... What most you tube commentssay to look smart

[@king39355]

could u solve this improper integral integral from 0 to -2 for 1/x

[@prathedragon9847]

Watch at 1.5x speed to save time!

[@aleeexisss00]

You are so awesome.

[@Puxladen]

thanks brooo

[@patrickjmt]

No problem

[@idknuttin]

what kind of pen was he using?

[@tommyommymmymyy]

+idknuttin twas a pilot Precise. BEST PEN.

[@beta5770]

nice problem

[@BLKro]

It's a Pilot Precise V5 ;)

[@どーくん-j2z]

this is ridiculous. I hope our prof doesn't give a problem as complicated as this on our finals XD XD.

[@MarkMcDaniel]

Intregration domination!

[@gddraftsman5617]

why you uses sec teta

[@Ytremz]

Beyond my syllabus but hey

[@Quichey2]

Diverges.

[@tylerchengabc123]

I know everything just watching the solution

[@alexthedude07]

This demonstration makes me fear for calculus BC as I'm still in year 1...

[@sunilagarwal712]

Wow!!!

[@gyaltsentamu6728]

It's just simple method

[@rohankhubchandani3694]

that was scary

[@hitomihoshino467]

He put bunch of something like this on the last exam and no one passed 😭

[@buddies4life66]

Woo

[@TwisTeD913]

OMG SOMEONE HELP MEEE

[@MrMr2012believer]

insane

[@chirayudesai793]

Find the anti derivative of that😂

[@kanivakil198]

Is this answer correct: online integral calculator disagrees.

[@NazKam]

you know what youre cute lol i hope youll reply to this :P