Indefinite Integration (part IV)

[ABCba5tard]

sal, i actually find ur old videos more helpful than the hd ones.

[Kcvee777]

wait nm, all good

[Kcvee777]

k im confused, what happens to the 2x+3!!!??

[richjammcl]

@Kcvee777 Reversing the rule he multiplied the equation by 1/the derivative of inside the brackets which was 2x+3. (1/(2x+3))*(2x+3) = 1

[123aellis]

I'm in the middle of learning an entire semester of University Calc 1 in 2 days... Exam is in 41 hours, I'm gonna ace this shit. :)

[Kcvee777]

@123aellis lol... mee too sun

[MegaZambam]

just thought i'd point out you're writing mu, not u. It's not a big deal, I'm sure everyone knew what you meant, just pointing it out!

[palepumpkin]

Why can we cancel out the dx's if du/dx is not actually a fraction?

[abhishekjainxyz]

Its ok

[lafyguy]

hmm i will do it over here to make it extra messy

lol 5:50

[tweety32312]

Wow I actually get this now. It's so easy!

[DelGeeZee]

I thought the dx in the integrand was dummy variable???? But I see you use it in your video and multiply by du/dx.

[6BURG9]

i just about died when you sneezed/coughed in the mic haha i have you on full blast in my campus cafeteria

[6BURG9]

my prof taught us to substitute like this

du/dx=cosx

so du=cosx dx

then subthat back into the function and differentiate with respect to x

[IamJacksColon4]

how about (sinx)(lnx)? is a more suited instruction on reversing the chain rule.

[trecool212]

@aolyahoo Wait. You're trying to tell me that Sal Khan is the instantaneous slope of your Russian calculus teacher? Can you show me your proof of this?

[aolyahoo]

Sir you are the derivative of my Calc professor. He is Russian and makes stuff all complicated. You break stuff down and simplify the learning process. I very much appreciate your help. You are the reason I am passing calculus.

[trecool212]

@aolyahoo it appears that you're still a little shaky on exactly what a derivative is...

[aolyahoo]

@trecool212

(Calc professor)^prime = Sal. It appears that you are in over your head! Its a simple concept. if you need help on what a derivative is, you can private message me and I will be glad to help you out.

[koitheawesome]

For someone who is taking Calc II and wants to promote education as a valuable tool for all societies, I want to thank you. I have seen interviews with you as well as seen many of your videos and already I highly appreciate your contribution to society. I believe that making education more free for the general public is the key to global prosperity; and for that, I am infinitely in your gratitude. I cannot give you my thanks enough, except in words alone, but I hope that alone will suffice.

[Charlietheleet]

math is fun when u watch it but even better when u solve one by yourself :)

[bobcatlow]

Thanks so much! this video really simplified it for me :)

[tylittle12345]

I'm actually stuck on a problem that I need help with. How can you integrate rational functions. The problem I need help with is: Integrate 9sin(sqrt(x))/(sqrt(x))

[tylittle12345]

@tylittle12345 Oh and u = (sqrt(x))

[MetalQuarantineMusic]

LOL AT 6:43.... sorry...I'm so mature. :P

[mizzou4life1993]

@MetalQuarantineMusic i dont get it

[TheNewAgeHippie]

So in the last step what happens to du?

[Breezyy527]

rememorize.....

[giulliabreis]

mind blowing indeed! thanks so much for making my life happier :D

[Diviniteee]

Guys, it really helps if you pause the video and try to solve it yourself, then play it and write down the work Sal does and compare it with what you did before to see your mistakes

[AsakuraAvan]

im not getting the right answer by using "u-sub" with integration of (e^x)^-2

[hahs4]

can anyone please find the integration by substitution u=ax+b

x(4x-10)^0.5

please reply asap

[funnyfootlong]

6:42... Sex!!!!!

[USCSoundCheck]

~ e^x dx = e^x + C

~ sinx dx = -cos(x) + C

[USCSoundCheck]

Most important integrals to memorize:

(assume ∫ in front of term on right of equal sign)

- x^n dx = x^n+1 / n+1 + C

[shapeurmind]

In my opinion the first example is much easier to solve using substitution rather than the chain rule (this one got me a lil confused in the lat vid)...

[SomeApplesauce]

6:42 hahahahahhahahahah my calc class always cracks up when our teacher takes the integral of e to the x

[arykk]

what is the dx that always appears in the integral?? He never explained it.

[gilbertgodlyddd]

@arykk The dx means with respect to x. For example the integral of 13x with respect is 13x^2/2 when you integrate with respect to x. If you had 13y, you would need to integrate dy, or with respect to y. It just shows clearly which factor you are integrating with respect to which becomes useful when you have multiple variables.

[EchoMillennium1]

Let me let u equal this function

[allsmiles432]

I'm actually in disbeleif that I understand this. God bless you.

[ixlOvexmyseLf]

very helpful. :)

[woo216]

integrate sin(x)/x

[shaneymane15]

@woo216 That's not possible with simple calculus.

[woo216]

@shaneymane15 why not calculus is beautiful and should be able to handle anything!!

[shaneymane15]

@woo216 lol yeah but you need to use a Taylor series to solve that particular integral

[Has9H2O]

can you please help me solve these two u-substitution equations? it goes like this:∫ [(1+sin x)/cos x] dx where u = sin x and ∫ (sin x)^3 dx where u = cos x. I'm having trouble trying to solve trigonometric functions by substitution...any tips would help a lot...i don't get what i'm missing...

[umeirdestination]

@Has9H2O the thing with it is that u shuld break up the equation as follows: ∫ (1+sin x)/cos x dx = ∫ 1/cos + sin x/cos x dx this implies that u can integrate each of them seperately and add the result. ∫ 1/cos x = ln |cos x| + c and ∫ sin x /cos x using the substitution u=cos x, u will found out that sin x cancel out. Hope this help.

[rainman8367]

o no it's getting harder, but a lot more understandable than my useless math professor.

[Tasan0315]

Dude thanks a ton for the lessons. You saved my integrating butt with these!

[ZnBangash]

the lastest comment was 3 months ago? Let me "refresh" the comment section: Thanks for another great video Sal!

[Thymonico]

Hmmm. I'm not sin x!

[fateater77777]

all your doing is engineering problems that allow you to use basic substitution that anyone understands, you should do one, where du/dx does not just happen to cancel

[madscirat]

I wonder if simplifying before integration is risking information loss in an equation. Im always paranoid about that.

Great as always, Sal. So looking forward to definite integration. Area/Volume of all 3d shapes shall be MINE!

[waaaasupp]

You are awesome! Thank you so much!

[zonedout245]

Thank you so much.

[Thymonico]

Has he gotten to the part where he proves that (d/dx)sinx(x)=cos(x) ?

If so, where is it? :)

[kamex2007]

Man! I've been searching and searching for a video that gives the "reason" for the "substitution rule." almost everyone who makes a video about it doesn't talk about the reason, they just jump into saying, " well let's substitute this gynormous equation with U" without explaining anything. Now on your video the "Reverse chain rule" concept explains the reason behind the substitution rule. This makes a world of difference. I think.

[crisgisvic]

Hi Sal! You've helped me a lot in math!! I learned calculus because of you. BUT!! I have to comment that in this video the last indefinite integral might be wrong...

Isn't the antiderivative of: e^-2x = -e^-x ???

Thanks for the videos, you are the perfect teahcer!!

[sabriel80]

let me equal sinx? lol

[MichBich1234]

im preaty sure cookies make math fun

[CPLains]

fun makes fun fun

salfun

[jerronimo22]

calculus makes man futh.

[xUltimaProductionsx]

Thank you for this video... I spent hours trying to understand the substitution rule, since my prof's notes are extremely confusing. This makes it seem so much simpler. Thank you!!

[lensman1781]

Isn't math up to Calculus learning rules, and Calculus learning how to make up cohesive rules

[MonoFocus]

It's a good way to put it. A Swedish mathematician once said that "integration is an art form while derivation is craftsmanship" because you can always find the derivative by using rules, while integration often times requires imagination and experimentation ;)

[iluvaginas]

English makes fun math

[Dan48p]

@iluvaginas no chemistry makes math fun

[BigPurple121]

calculus makes math fun

[xlwaiyiplx]

algebra makes math fun...

[BigPurple121]

Algebra is a language, calculus is actually useful

[roller0coaster0gal]

Algebra is the alphabet of Calculus

[wesselbindt]

Not only of Calculus.

[Talo001]

Fun math makes calculus

[Grobannela]

For me is more easy to write du=(2x+3)dx...

But, is the same so...

[TurnyWurny92]

argh im not lookin forward to my C4 exam :[

[kickit246]

how did it turn out? (if u did it yet). My calc exam is on saturday i believe. :(((

[TurnyWurny92]

mine's not till June luckily, so many joyful hours of revision to come ;(

good luck in yours though!

[kickit246]

haha awesome, i wish i had stumbled on these videos earlier! :( Comp sci on thurs and calc on saturday! Blah! Thanks tho, gonna need it!

[belal1988]

how did u know that (ex)-3 is the u ? why it's not the du

or in other word

in difficult ones how can i know which 1 is the u?

[d3c4p3t4t0r]

When you take the derivative of 'u', you get the term you don't call 'u'.

[Beefstew2011]

Yeah, the thing about these problems is that they are heavily engineered so that one of the terms in the integral is being multiplied by another term which just so happens to be its derivative.

[QuantumMaths]

No, its just setting up so you can reduce general derivatives using integration by parts, trig identities, etc. so you CAN boil it down to a u-substitution even in general integrals about 95 percent of the time.

[iluvjiyongx3]

i was confused on the previous vid, but now i think i get it!! omg, this is so cool! thanks a whole bunch! ^^

[gamemaster014]

dude the integral of e to the x looks alot like sex lol

[darkfighte]

ooooooooo..now I get it..lol..the vid before this got me slightly confused, but its good now.

[rohan123444]

is it free to enroll in your academy??

[kikisammy]

Nice job - but those colors - Ugh! I'm going blind.

[nameless8908]

great job, keep it up

[djfirekid]

I offer many thanks

[bradkey98765]

I will also switch colors just to keep things interesting, Lol

Another great video, but i'm still yet to solve the anti-derivitive of (x^2+1)^(1/2) The square root of (x squared + 1)

[WPM1414]

THA CHAIN RULE! At least, i think. I know that this comment was posted a while ago, but i'm curious too. I believe you would use the chain rule, but i am not to integrals yet in Calc.

[Theinvoker1]

Another great set of vids, the wall of text in the book is slowly becoming clear. Keep em coming! :)