Indefinite Integration (part III)

[BlowtheBridge]

I will stick with being a nice guy & a Patriot.

Thanks Ms. Delong!

[Alive4Metal]

u = sinx

du = cosxdx

[superg33k12]

Hey Sal, recently I've been getting into the golden ratio, the Fibonacci sequence, and the Lucas sequence. It would be really cool if you made a video about them and how they are all connected. THANKS :)

[Kaiyazu]

Even though Khanacademy is a nonprofit organization or whatever, you deserve many riches of the world for making future generations more intelligent and getting to college, if it weren't for you i would've never understood this. Thank you so much!

[Tito23892]

I have a exam of calculus in 6 hours, omg i am fucked.

BTW thanks Sal for this amazing videos

[ghattan117]

The one concept from all of his vids that I still can't understand :( YOU'RE STILL GREAT :)

[jaymejamjar]

ah, i'm still confused. these stupid integrals will be the death of me.

[MementoMario]

@MarkSkrams You're completely right, good call there.

[colton004]

SALculator to the rescue

[Vlardez]

who else was shitting themselves when they saw just ln^2?

[mypassisincaps]

a person who can make it look so simple must surely be a genius.............

[MarkSkrams]

3:20 should there be an +C right? please correct me if im wrong. thanks.

[ranpo677]

Just may stand a chance to pass this damn class thanks for your work.

[WHY70122]

PIAMBO: it took me almost 4 hrs to go all the way back from the beginning of cal 1 and i got it afterwards....it was a great thing to understand that after some hard work...The way i worked it out was to do the chain rule in both ways. Anyways, thanks for explaining it to me though buddy.

[WHY70122]

This is the 1st time im confused about ur vid... i mean the second example.

the integral of (cosx)(sinx)^3 dx. i understand the chain rule but it seems so complicated in this problem. The integral of (sinx)^3 = 1/4 (sinx)^4...this is true but where's the cosx gone? plz respond to this question cuz i, trying to review my cal 1 before i get to cal 2.

[TheNewAgeHippie]

My teacher knows I watch your videos because I solve for g'(x) before I do f'(g(x))

[supercalifragilismic]

i wish you used simple example for reverse chain rule >_<

[dinmorerengeit]

what happens to the cos and tan if you take the derivative of cos x or tan x?

[moha044]

Maths are so simple on this video :D

[Seguris]

@moha044 And it seems english is so hard on the internet ;p

[USCSoundCheck]

∫cos(x)dx = sin(x)dx

[USCSoundCheck]

∫1/(x) dx = ln|x| + c

a^x dx = a^x / ln(a) + c

[USCSoundCheck]

∫sec(x)tan(x)dx = sec(x) + c

[USCSoundCheck]

∫x/lnx dx that sounds fun

[zingleband]

hey??

can you answer this ?? integration xdx/ln(x)

[snay33]

can you be my tutor?

[EchoMillennium1]

You're a god.

[manoj311093]

can anyone tell me where the 1/x goes in the sum in the sum Lnx2/x!

[EchoMillennium1]

@manoj311093 no no i think ur confused just like me initially; it doesn't go anywhere, it' disappears. the reason why this is so is because it is already the derivative of lnx^2. thus, u can treat the lnx^2 side of the function only.

basically u ignore the 1/x part and take the integral of the other side

[manoj311093]

can anyone tell me where the 1/x goes in the sum in the sum Lnx2/x!

[manoj311093]

can anyone tell me where the 1/x goes in the sum in the sum Lnx2/x

[Soviless99]

where the hell does the 1/x go

[shawnk82]

4 dislikes, really? Sal is amazing, all he needs is an app for my iPhone, oh wait he's already got it, haha... please keep going Sal... your vids help a ton

[denni0302]

I had this type of integration question in my trial exam. it was a bit simpler than this though, it was x(10-x^2)^(1/2). i was sitting there thinking how the fuck do i do this and remembered afterwards that the x is the derivative of the inside of the function (times -2). we get taught to use 'u' and make u = 10-x^2 but that shit is confusing as hell.

[nikanj]

You've completely lost me with this one Sal!

Oh well hopefully it gets clearer in later videos.

Thanks!

[nerrrus]

mateee i dont know how to thank you, iv only been to class about 4 times beacuse my lecturer cant teach if his life depended on it, and im gonna pas all beacuse of your,also you passed me in proability and statistics and phyics, you are a legend! somebody give this guy an award of something man

[danstone1991]

cheers dude for this video, realy well explained.

[enjoyablesounds]

i wish everybody would stop using the prime-notation...

[p1n0yXer]

@enjoyablesounds i like using prime notation, leibniz (spelling) notation is still a bit confusing to me

[enjoyablesounds]

@enjoyablesounds u know what nevermind...i just need to practice more

[OneNonlyME1]

God Bless you!!! I was soo confused about the u-substitution method till i watched this!!!

THANK YOU!

[angelsarah7]

awesome, so simple. thank you!

[chimrae]

You forgot plus C!

[amykrfq]

@chimrae loooooooool

[curtdiaz]

One quick suggestion... You should learn the keyboard shortcuts for inverting and clearing the screen. They're listed on the drop down menu!

[lilmaqi]

@curtdiaz it is because he sits a little bit far from the keyboard.

[EchoMillennium1]

@curtdiaz shut up; it's not even a distraction

[theredmars]

@curtdiaz great suggestion for a video that is 3 years old when you made the comment.

[Seguris]

@curtdiaz he's too smart for that.........

[esl21]

@curtdiaz There's a purpose behind this method, it allows the viewer to mentally relax their mind for a moment and start the next problem.

[Yujushi]

im mseeing up for the first time =(... but i KINDA understand it... good work still sal

[khalidwalankar]

U CONFUSED ME FOR THE 1ST TIME!!!!!!

[FloridaCarClubcom]

Same

[ILockItDown]

lmao

[MunchVids]

Yeah, I was too but I looked back at some parts and I wasn't so confused.

[himynameismac]

"Acually let's do that, let's do that. Oh no, no, no, no, I don't want to do that now, 'cause that would confuse you" :):)

So nice to have someone that can explain stuff like this without having the "I know everything and never make any mistakes" attitude. Keep up the good work!

[marcusjhung]

XD plus C, dude

[sammok83]

sal, you are the best..wish you wer my calculus lecturer..i would sure score for my calculus.but i still do not understands the last question..you got 1/4(sinx)^4 because of intergating (sinx^3)..but what happends to the (cos x)..pls help..thank you soo much...thanks

[digforbear]

@sammok83

since cosx is the derivative of sinx then you can use the chain rule in reverse, watch this video and the previous one again, hope this helps!

[iSlamIcBrOthEr1]

He is AWESOME, I wish if he were my teacher for this quarter,,,,,Good job

[g1code]

hey there , forget about the last comment , ur doing some good charity work ;)

now i have to be very honest ... i watched all the videos of MIT channel in calculus , but this is much easier and much more comforting

cheers

[sponsoredwalk1]

That is so true! I got so fed up with MIT's single variable calculus course that I came to youtube for a little clarity and was stolen away by these video's. This set of video's is too perfect. It's like your very patient friend who's good at math taking the time to sit down with you and explain, using examples.

[EcinPC]

MIT's calculus starts assuming you know limits. To take calc there, you would probably have to take calc1 in harvard as a remedial. But most students in MIT have taken calc 2 in AP.

[Budisawsome]

O.O

[ranma54]

whaaa..?

[HANNONKEVINP]

Does it matter if you start from inside and work your way out? Or do the opposite and work from outside in?

I learned to do outside in.

[BigPurple121]

Think about the ramifications these videos could have on places like Africa & some of S America where people now have access to teachings of moderately advanced math, or at least enough to pass any entrance exam. I wonder how the internet will pay off in increased human capital in 20 years

[aubreydavid]

Thats a very interesting economic question you know! I'm sure these videos will break it way down to whoever needs to learn. All they need is to understand english.

[USMChiLD]

iono what u talking about. All my cousins from south america always kick my ass in math. only thing i'm better at than them is English, haha. And I'm pretty descent at math, thanks to Sal.

[2112titus]

totally natural sounding teacher. awesome job

[Beefstew2011]

I hate integration because you have to use numerous tables for it and it can't be calculated nicely in most cases :(

[cristianhdzhdz]

do you have any examples when the "S" symbol has a number on top and another one on the bottom, somthing like this: 2

S (2x+5)dx 1

and you also have to substitute something like this b-a

/\x=-------- n

ci= a+i(/\x)

and it has a limit

lim

n-->OO(infinite symbol)

can you help me?

[weeno777]

those are definate integrals

[Gaussdxdydz]

Sorry I'm a bit dizzy. Ignore my last please

[Gaussdxdydz]

Hello Sal. Great video. Although at 4:24 I think you meant (lnx) squared, rather than just ln squared, right?

[lookwhoscomin]

4:53

[zeeiggy]

i understood that perfectly. thankyou.

[jontyhopper5678]

you are really an excellent class and you way of explianation is simply the best

[btboyd90]

Sal! You finally forgot the +C (on the last example)! No worries, you're still the man.

[DanneMan80]

Great explanation! Been struggling with this one page about substitution techniques all day and you explained it in 5 minutes. Thank you!

[bangalirussian]

sal is da best!!

[daydreamer019]

Thank you very much! ^_^. Is your name Sal? cause you kind of mention that in this vid or in the other ones. But, hehe. Just curious. Don't mind me. Thanks again!

[clerlic]

You're an awesome teacher, I bet you could even teach advanced math to a 5 year old :D

[citrizz]

shouldnt this be 1/4(sin x)^4 + C?

[Stefovic]

The integral rule isn't the same for composite functions as for conventional functions. Othervrvise your method is right.

[daydreamer019]

But is it still right if the answer always has a + C?

[nameless8908]

this is a pretty good review, but i had a little problem with the order. when you were taking the derivative of the composite function, you initial began with the inside and worked ur way out. but since everyone is taught differently, we would initially take the derivative of the outside and work our way in. but it helped. thnx