Integration Using method of Partial Fractions

[Alive4Metal]

where does the single x term come from? im confused

[attentionwhoreusa]

why is the first term A/x? shouldnt it be A/x^2 ? Where are u getting the lone x? thanks

[hmlsport]

@attentionwhoreusa, its A/X because when you break up the equation into partial fractions, the rule is to break up x^2 to (A/X)+(B/X^2) and so on, its just how the rule works for solving partial fractions

[8644371]

Whoa-whoa-whoa! I got A=-1. And I did it the long way. And I checked it on my calcultor (I let x=2). [Also: I'm viewing this on my iPod Touch. So: if there are any annotations correcting this or a lot of older comments already pointing this out. Then my bad. I can't see it.]

[MultiMoe91]

is the corrected video available?

if yes please link me, appreciate it :)

[Kratos0909]

this video is just incredible

[patrickJMT]

@Kratos0909 glad you like it ; )

[trese0000]

Patrick! You just don't know how much you have me feeling so comfortable with partial fraction decomposition. When I went through Calculus 2, I learn it just enough to do the problems, but still was weak with it foundation-ally. I watched 3 videos thus far, this being the third and I feel like a pro at his stuff. You explain it OH SO WELL. I can't believe all this time I was scared by it going through my math classes, and when I hit ODE's, I needed it once again. The dread, but made it out fine.

[sejones42]

Thank you so much for all the videos you post. I have really learnt alot and also a great revision tool. For this video in particular, what is the final answer you found? Just so i can see whther i got the final answer. I'm sorry if you have already replied to a similar question but i've had a look and haven't seen one. :)

[janedoherty101]

what if instead of the denominator having a squared expression it had a squared one? ie (x+1)^2 vs. (x+1)^1/2?

[patrickJMT]

@janedoherty101 do you mean a square root instead of a squared expression? if so, that totally changes the problem. it just depends on the problem at that point. in the case you mentioned though : (x+1)^1/2, you can do a rationalizing substitution in some situations

[davidh1155]

Sounds like you have cats?

[blackcard00]

Thank you so much. You talk to me rather than repeat from the book and show answers, unlike my professor. It is much easier to pay attention and stay awake to. Thanks a ton.

[festexi24]

Thank god for this video, it looks so simplistic but the lack of variable up top just sent my head spinning!

[DucCN01663]

Wow, lefthand writing

[wintermonie]

u didnt explain integration by partial fractions u just did an example ... i still dont get it :(

[patrickJMT]

@wintermonie ok

[lilangel0072]

@wintermonie r u serious? he was to the point and explained it nicely, plus this is the easiest stuff u're gonna learn in calc, if u don't get this then maybe u should reconsider ur classes.

[chadbowman0]

@lilangel0072 That's total BS, this stuff is a bit complicated. Because of the algebra involved.

[lilangel0072]

@chadbowman0 there's waaayyyy harder stuff in Calc 2 involved, this stuff isn't only easy by comparison but it IS the easiest this class is gonna get...honestly take it from me, if u can't do this, don't bother with the rest of the course.

[chadbowman0]

@lilangel0072 I took Calc 2 years ago. You are ridiculous.

[lilangel0072]

@chadbowman0 then why r u searching this video? i see they didn't teach u well back then.

[lilangel0072]

@chadbowman0 I took calc 2 last year...and it was easy, this also happened to be the easiest part in the whole course. Just because u found it a challenge doesn't mean it is one.

[mlcarter815]

@lilangel0072 Why are you such a douche?

[IvanGangsta1]

the people who don't like this vid are the ones who don't understand it!!

[lilyvoon10]

why would it be Dx+E?

[The3jji]

@lilyvoon10

@lilyvoon10

Well, the denominator has a (1+x^2).

So, the nominator should be (D x+E)

Refer to previous videos if you don't understand

[gotahope]

Thanks mate, this is such a good help 3 days before my HSC exam :)

[MillerTivo]

I know this is the 5th time this question is asked, but there are no responses:

Why is there an A/x term when there is no "x" factor? The factors are x^2, (x+1), and (1+x^2), so shouldn't the terms be A/x^2 + B/(x+1) + (Cx+D)/(x^2+1)?

[patrickJMT]

@MillerTivo x is a factor of x^2, so there is an 'x' factor

[AlecWangable]

@patrickJMT why is the denominator for B x^2 then if one x is already being used on the A

[Ichneumonidae2]

@AlecWangable When decomposing anything raised to the second power you have to repeat the variable. So, if you were decomposing (x+1)^2 it would be A/(x+1) + B/(x+1)^2. The reason you do this is because if you only write one fraction (e.g. A/x^2 w/o also adding constant raised over a denominator "x") you will be missing a factor of whatever is being raised. Try decomposing 1/x^2(x+1) by only writing A/x^2 + B/(x+1). You'll come up with the wrong answer b/c you would be missing a factor of x.

[raptor2000raptor]

@MillerTivo

The x^2 factor in the denominator is a linear factor of multiplicity 2, so you need two

terms in the decomposition, namely A/x + B/x^2. In general, a factor of the form

(x-c)^k will need k terms:

A1/(x-c) + A2/(x-c)^2 + ... + Ak/(x-c)^k

[sirsideways]

@MillerTivo it is considered a repeated factor, giving A/(x) and B/(x)^2 as with all repeated factors, however in this case the factor (x) is x itself instead of something like ax + b. It is not a linear term, or an irreducible quadratic hence why that expansion would be incorrect.

[shirleybreeze]

why is there an a over x

[DashofDosh]

Okay. sooooo I used Dx+E in the beginning, so how would you go about solving for A, D and E later on in the problem? Do you use elimination or substitution?

[patrickJMT]

@DashofDosh you can use either method

[TheSamus1992]

youtube is one of the best ways to help with my homework

(as long as i dont get side tracked)

[nealogz]

OMG thanks a lot. 

[buddymorganjr]

This Guy is a Genius! Thanks Patrick!!! :D

[JTosser]

Hi Patrick.

I know that the answer to the integral of 4x/(x^2 + 1) is 2ln(x^2 + 1) but i have no idea how the 4x becomes 2. Do any of your videos help with this?

Thanks

[ryezizzle]

what god did you pray to to get so good at math?

[patrickJMT]

@ryezizzle none. i studied.

[lmfaowtfinghell]

@patrickJMT HAHAHA amazing answer lol

[buddydog1956]

I'm studying for the FE Civil.... thanks for your videos!

my favorite, nonetheless was ODE's! ... PDE's (don't ask!!! they're killers!)

But Keep the work coming, You're the Man!!!

[pricesalem]

good example, very helpful, clear and concise explanation. THANK YOU!!!!

[patrickJMT]

@pricesalem no problemo

[sabrinanne]

why didnt you use Dx + E on the fourth term?

[spellmaster91]

0:19 -- I don't understand, why is there A/x, instead of an A/x^2?

[lucile1010]

whou you're so cool!

that's gonna help me alot when im being lecture tomor.

='DD

PS;/ I love your writing!x

[jonpbody]

i've learned so much from you man, thanks so much for making these videos for us.

[fttank]

nice stick people drawings :D

[tigerinatunnel]

you're probably one of the best people i've come across when it comes to explaining math. thank you so much! you've definitely saved my life more than once when it came to midterms and finals. :)

[Neverdii]

thanks for being one of the only people willing to volunteer their time to help others with math! I wish there were more people motivated by helping others instead of by money like you...it's a huge help man, thanks a ton

[metalfreak1892]

heyy mann... im a guy so i cant marry you..but i'd hook u up wid one of my female friends....

that helpedd soooo muchhhh THANKS

[rollindarwin]

man u just make my life so damn easy :)

[kalemarefrite]

i should buy you a drink :)

tnx alot!!!

[skyfaze]

you can donate to him on paypal!

[nickistheman12345]

Why dont you multiply the A by x^2 and the B by x?

[nickistheman12345]

Why is there an A/x in addition to a B/x^2  ?

[ghostman515005]

cool... left hander...

[platanoproductions]

i don't understand why he set both A+C= 0 and A+B+D= 0

[donedwii]

please be careful with your parenthesis..

[Stepdenisethetrumpet]

how do you know to plug in 0?

[ghostman515005]

most of the time we plug in 0, -1, 1

[andyct1982]

i dont mean to sound rude but not putting Dx+E in the equation makes the rest of the video hard to watch. why not a redo? mulligan?

[hyky68]

ehh so.... in the beginning, why do we need to have the a

A/x term when there's really no single x value in the original equation?

[jindassasin]

it's people like you that give me hope for humanity

[patrickJMT]

ha.

i often find myself disliking humanity so much, i wonder why i make these, and wonder if one day i will just take them all down... : )

[bryandPR]

no patrick no! theres a few of us who are really thankful for these videos!

[patrickJMT]

ha! do not worry : )

99.99% of the youtube comments have been so amazingly nice that my faith in humanity is being restored : )

[JillKellLou]

Yay! So... Um, when's our wedding?

[nickistheman12345]

DONT!!! please. I really appreciate all of your videos... just so you know.

[Mike3smith]

why is there an d over 1+x^2  it should be (dx+e)

[patrickJMT]

yes, absolutely.

a few others pointed this out; i have added annotations pointing out the mistake.

thanks for pointing it out!!

[trevort888]

why isnt it just D?

[abuckajaga]

Because there is (1+x^2). The problem is the x^2. When you've got x^2, you must write Dx+E (not always Dx+E, of course - it can be Gx+H :-) )

[axelasdf]

Where Can I find the corrected video?

[axelasdf]

... I did it all without the "trick" at the start where you set x=0 and x=-1, where I just multiplied it all out and solved using equating of the coefficients, and after all was done, I got "1/x^2+-1/x". Did I carry this out correctly? Would you have gotten the same if you had multiplied out completely / didn't substitute in your values that you got from your "trick"?

[totlolrofl]

Great video, thanks very much

[k0tiak]

Are you sure the last term isn't Dx + E in the numerator? Usually if (b^2 - 4ac) for the factor is negative, you use Dx + E (or whatever letters/variables your using) rather than just a D.

(0^2 - 4(1)(1)) = -4 which is < 0. For (x^2+1)

[gekaizer]

I agree with what you are saying.

[patrickJMT]

ops yes,i will have to fix this!

[Bigpappy619]

how did you get A over x when you were starting off?

[patrickJMT]

that is the partial fraction decomposition for linear factors... i have a video on my website explaining that step if you feel the need to check it out!

[patrickJMT]

yea, partial fractions is a long procedure unfortunately! hope it makes sense though!

[jonwalker80]

whew, long but good!