Integrals: Trig Substitution 2

Another example of finding an anti-derivative using trigonometric substitution

[falubii]

Sal really went off on a tangent with that derivative.

[moohendischi]

When khan starts not making sense to you, that's the moment you know for sure your screwed.

[lovelyleslie]

Your videos are life savers! I'm taking calculus and a university and learning far more from your videos than from my professor. Thank you so much

[lu-dxoh]

khan is usually good at simplifying math he makes it more complicated than needed on these videos

[AlexanderKoziol]

I'm 14 and I'm probably obsessed with math. I've learned so much through this and textbooks from the library that I probably won't have to *try* in math until college. I'm going into Algebra 1 in 9th grade, but I solved this problem on my own, halfway through the video. Khanacademy is great (so is the library).

[MagicDiner]

Thank you so much for making these videos Sal. You may be the only thing keeping me sane in college right now!

[reyrey]

hey this is a very good way of doing the integral, but the problem can be solved in less than 2 minutes if you use integration using inverse trig functions, i.e. d/dx 1/a * arctan(u/a) = 1/(u^2+a^2) , so 1/a * arctan(u/a) is the antiderivative

[woodenjaw]

I have to say you make this stuff seem like fun, It's almost 1AM and i can't sleep because i want to keep learning.

[universe]

I just want to say the blackboard tool you are using in this setup looks cool and clean and very easy to follow. Though the chunky messes from the past videos were just as much fun. :-)

[geodude]

@ 1:13 since this is the arctan formula, i learned that x^2/36 can be rewritten as (x/6)^2, and if u pull the 1/36 out of the integral u are left with
1/36*integral[ dx/(1+(x/6)^2)]. Now with u substitution u can say u=x/6 --> du=(1/6)dx -->6du=dx. substitute back and now u get 1/36* integral [6*(du/1+u^2)]. pulling the six out leaves you with 1/6 and now 1/(1+u^2) is just arctan(u)*1/6 --> which is 1/6 * arctan (x/6) --> (u=x/6)

[gobberpooper]

"cuz i don't really remember the quotient rule. i've told you in the past that it's somewhat lame..."
LOL
And yes, I too am addicted to this, partially because of his voice

[huseynbabarzaquliyev]

Thanks so much, tomorrow I'll have an exam, and I didn't know how to solve those problems, now I think I can:)

[StreuB]

stuff is beautiful. I would have never seen that, but when it starts coming together at the end and you begin getting cancellations, you just giggle and smile.

[adityangrj]

Took calc ab in junior year and will take calc bc senior year. Watchin this vid made me realize how much calc I forgot. This vid'll help me refresh before calc b

[anitharajendran]

we can find the answer without substitution using the standard result- integral 1/(a^2+x^2)dx=1/a arctan(x/a)+c.

[Hadee]

Is it just me or when ever kahn explains something in calculus the calculus becomes too easy, either way khan rocks the infinity :D

[janvisagie]

TY you explain it in a way I can understand it rather than having memories and regurgitate it

[borob]

At 2:57 why is it not plus minus if you square root both sides?

[ASR_bagachump]

Actually you can substitute x=6tan(*). Then
dx /d(*)=6(sec^2(*))d(*)
then dx=6(sec^2(*))d(*)
then integral becomes {6sec^2(*)d(*) /36(1/(1+tan^2(*))}
This gives integral of {sec^2(*)d(*)/6sec^2(*)}
Which gives integral of 1/6{d(*)}
This becomes */6 which is the answer. "*" can be substituted by arc tan(x/6).

[wagnersantarosa]

thanks so much. You make it seem very simple and understandable