A Complete Partial Fractions Problem

[Shkencetari]

This is a great video, really, a very clear explanation.

[SenorEncurtido]

My calc2 teacher literally goes from the beginning to the end, never showed us how to find variables or anything. Thank you

[SpnFan04]

HUGE HELP, thank you so much!

[sarahsissons]

Thanks for this video, I'm sitting a further maths paper tomorrow afternoon and this has really cleared up the equating the coefficients section for me. :)

[patrickJMT]

@sarahsissons happy i could help : )

[SwissRevolver]

Is the integration of 1/(x^2+3) dx incorrect?

Algebraically.. pulling a 1/3 out leaves 1/( (x/sqrt3)^2 +1) dx

Substitute (x/sqrt3) for u, du = dx/sqrt3

Isolate dx, so sqrt3 du = dx

Substituting and pulling out the sqrt3... sqrt3 /3 integral of 1/ (u^2 +1) du

Cleaning it up = sqrt3/3 * arctan(u)

Cleaning it up and substituting u back in = sqrt3/3 * arctan(x/sqrt3) +C

[Murtiniadis]

Coincidencely, I find you Patrick! I am a Turk and 2 hours ago, I got private lesson for my MATH104 Midterm 3. I paid a lot of money. He told me this lesson with Turkish and I understood nothing! My english is not excellent. Naturally, My Turkish is better :) but I'm understanding you easier! THANK YOU FROM ISTANBUL!

[frenchsaber]

thumbs up if you're watching this half an hour before your final exam...

[noneabove1182]

YOU ARE THE BEST! I have my calculus final tomorrow and did NOT understand this at all!!! Thank you so so so much!!!!

[jazjaz1313]

omg life saver

[sastido]

I never go to my Calc class!

[tupacsomething69]

where is your nobel prize?

[patrickJMT]

@tupacsomething69 in a different universe

[BANANAENDMANDARINA]

@patrickJMT Hahaha, so you need to find particular solution to get it.... Joke... =D , man your vids helps a lot, Thank you

[EvilDaggerzx]

someone can please tell me? i am taking GCE O levels this year and i am wondering whether it is allowed to use e.g. let x=5... the books i use always use the method of expanding and factorising so that e.g. (2A+B)x^2 + (A-3B)x...

[fatshadow92]

@EvilDaggerzx

There are two different thought processes (maybe more) that are popularly used to do partial fraction decomp. One is more technical than the other, but they both give you the same result so it doesn't matter. Whatever makes sense to you.

[mxdog45]

fking love you, helped me out understanding this.

[bigbob12342]

can you tell me why you put Bx+C and not just B at 1:02 ?

[TVInformative]

@bigbob12342 that's a great question.. He did not do a good job explaining that. My professor said something about it being a complex term im not sure. I was hoping Patrick would explain better. I always get it wrong for using the incorrect B or BX+c .

[hen555]

@bigbob12342 you have to do a Bx+C because the denominator has order of 2

[MultiMoe91]

i'm missing classes and i'm not worried at all :)

[ShrodingersPerson]

oh patrick i love you.

[patrickJMT]

@ShrodingersPerson ha ; )

[KillerZero259]

@patrickJMT hey patrick, i've noticed you never say "i love you" back to your fans. any reason why?

[sha31337]

How did you integrate 1 / x^2 + 3 ?

[patrickJMT]

@sha31337 use arctangent

[sha31337]

@patrickJMT Could you please do some videos on Bernoulli D.E

[hen555]

@sha31337 do Bernoulli Differential equations please!

[PandaMagicFTW]

@patrickJMT Yeah I didn't really get the arctan part either. =[

[lillibeth13]

@PandaMagicFTW it just turns out that the antiderivative of 1/x^2 + a^2 is arc tangent...

[hen555]

@sha31337

Integral (1/(x^2+a^2)) = (1/a)arctan(x/a) + C

Memorize/Remember that

[sha31337]

@hen555 i got ya thanks but why 3 is under-root?

[hen555]

@sha31337 It is because if you compare the equation 1/(x^2+a^2) with 1/(x^2 +3) then that means a^2 = 3 . Therefore a= sqrt 3.

Another example: 1/(x^2 +4) , in this case... a^2 =4 therefore a =2.

hope you understand lol

[brettmfm]

@patrickJMT I was wondering in this problem exactly how you got (2/x)? I understand that A=2, but don't understand how you did that step. Thank you for the video's, and if you could reply that would be excellent. Thank you very much,

Brettmfm

[Gavlar92]

So you say I need to use long division if the order of the numerator is equal to or larger than the denominator?

I've got a question on my university algebra past paper here that has a 4th order on top and a 3rd order on the bottom, but it specifies that I need to use partial fractions?

[drewpasttenseofdraw]

MOVE YOUR HAND!!!!

[tiff4annie]

why is there sill a C term?

[noobsonlypls]

is that an iron ring ??

[TheDrGonzoshow]

you helped me a lot here bro.... tanx ::)

[angieebe]

you're a live saver. thanks so much, i've been referring to your videos for the entire duration of my AP calculus course.

you rock :)

[millenniumf1138]

Fascinating; you explain it differently than my Calc prof. He had us solve A, B, and C at the same time by process of elimination, and you did A by itself, then B and C.

This is the thing I love about math: there's always more than one way to solve a problem, and if you don't get it one way, you may get it another way.

[jaboipell]

why did you put bx+c over x^2+3??

[asifbliss]

come and teach at the university of calgary!!

[luckypinkgirl007]

THANKYOU! my prof doesn't explain it like you do.

[jarekmrkt]

Patrick, You have contributed highly to my understanding of math and leave me no other choice but to blame you for my good grades!

Thank you

[djbeatzzz]

Your helping the world with your math, Your like a superhero Patrick!

[TheStephanie132]

hi i really love your videos. do you by any chance know how to solve partial sums of arithmetic sequences word problems?

[patrickJMT]

@TheStephanie132 pretty sure i have these already

[fadcAuTra]

how come you set x = 0?

[anol1258]

yea why the Bx+C for second term?

[wierdo5000]

@anol1258 because its a quadratic. you cant break it up.

[ronniemonnie]

Why did you use Bx+C for the second term? D:

[kmg05zero]

@ronniemonnie If the term has any power over 1 inside the parenthasis (I'm not sure of the mathmatical reason) you put Bx + C over it.

For example (x ^2 + 4) is over Bx + C while (x + 4)^2 would just be [A/ (x+4)] + [B/(x+4)^2]

[isaparisa1992]

thanks this is almost exactly like one of my exam problems!

except im not really sure why you used arctan in the integration

[aynakoitsroi]

lol i wish you were on youtube when i took calc in high school. i wouldve beasted all my tests. you're wayyy better than my calc teacher back in the days.

[iolakkaloi]

Why did the second term become Bx+C? Omg I'm lost.

[Naem9199]

the title said "A Complete Partial Fractions Problem"

and so i clicked it hoping to see how to find coefficient for long division

[TanaiG1]

Nice legs:)

[patrickJMT]

@TanaiG1 ha - lots of bike riding! : )

[BANANAENDMANDARINA]

@TanaiG1 LOL

[melonas22]

difference between you and any other teacher is that you say whats going to happen and what to look for. every teacher I have had just dances around the fire and never get to the point of what they are trying teach. I would like to thank you for helping me get a B in calc 1 and further helping me in 2!

[tooskool4cool]

so, when x is squared in denominator, u put x with the numerator variable and add the next letter (like Bx+C)?

[rhpsislove]

The problem I am dealing with is (4x^2-4x+3)/(4x^3-4x^2-X+1) and I don't know how to factor the denominator...can you help?

[tooskool4cool]

where did Bx+C come from?

i mean i get the B, but not the rest

[frenchfriesidiot]

@tooskool4cool the 'Bx+C' was written instead of just 'B' because the denominator was a quadratic and not the typical usual linear equation like 'x+2'.

[tooskool4cool]

@frenchfriesidiot

thanks

[sodaxcandy08]

ALL STATE CAN SUCK MY DICK

[gurdeepsandhu]

LAST PART OF THE VID IS WRONG, integral of 1/(x^2+3) is not 1/sqrt(3) . arctan(x/root3) since the derivative of 1/root3 . arctan(x/root3) is 1/(3x^2+3) not 1/(x^2+3)

[sultan009ful]

it is correct dear

[sha31337]

@gurdeepsandhu What's the integration of 1/(x^2+3)

[timechange01]

Thank you! This is extremely helpful. The words partial fractions scared the crap out of me until I watched this video

[linkinms]

x= Infinit

x * Thanks = Infinit of thanks

[eghatchi]

man ive gone through all your vids and they are great. but I cant seem to find one that can help me with this ...integral (x^2-4x+7)/(x^3-x^2+x+3) dx. heeeelp! please =)

[patrickJMT]

@eghatchi you just have to factor the denominator first

[unknowncreatures]

@eghatchi

google wolfram alpha

[bar95900]

Those Cox commercials are becoming really tedious!!

[patrickJMT]

@bar95900 that's what she said

[SAIL4323]

@patrickJMT

Some of my teachers dish out a month's detention for sexual sayings.

[18Zac1992]

You've saved my life more than 5 times now... Thank You!!!

[defendurrootz]

please can you go over that integral of x/(x^2+3) with me, I tried it but for some reason been unsuccessful.. and let me know when you've done it

thank you

[umeirdestination]

@defendurrootz youtube integration by substitution u will be successful

[Twentydragon]

I would not be passing Calc II without you, Patrick! Thanks! =D

[helloviolindonna]

thank you so much! this was incredibly helpful! 

[josuetrujo]

why Bx+C ????? HELP plz!! test tomorrow!! :S

[cyborgninja74]

@josuetrujo because you take the derivative of the denominator and that will give you a linear equation Bx+C

[cyborgninja74]

@josuetrujo because when you take the derivative of x^2+3 it will give you a linear term instead of a parabola, hence the Bx+C

[tensandtens]

I LOVE YOU!!!!! lol

But seriously, i've been struggling in math and this was exactly the video i needed to help me out with some extra credit. Once you explained to use A over something and BX+C over something, i managed to do the rest. I had been using just B before, which wasn't working. I love your videos, they actually make me want to DO math! =D

[aznelf13]

how do u remember the trig functions like how you just recognize the arctan formula

[alwaystvxq08]

ahhh, i get everything except in the arctan substitution for the last integral at the end... im getting a different answer

[AmerTheFarhat]

what would i put in the numerator for (x^2+1)^2 ??

[patrickJMT]

@AmerTheFarhat a generic linear term like Ax + B

[eva1304]

wait.... where did the tan come from!?

[patrickJMT]

@eva1304 i was out in the sun all day

[Syndicated4u]

@patrickJMT LOL. @eva1304 to find the integral of 1/(x^2+3) Use substitution and let u = x/sqrt(3)

du/dx = 1/sqrt(3)

du = 1/sqr(3)dx

Substitute. to get:

1/sqrt(3) * integral of (1/(u^2 + 1) du

the integral of 1/(u^2+1) du is arctan(x) or tan^-1(x)

this is probably where the tan came from :). Hope it helps.

[coolmafiaboy]

@eva1304 tan as tan, or tan as tanning << HAHA!

WIN OR FAIL?

[skatefallen91]

Awesome. Thanks for the help!

[mindann]

When do you use completing the square when integrating?

[patrickJMT]

@mindann you sometimes have to use it when doing trigonometric substitutions; if the quadratic under the radical has a linear term, then ya gots to CTS

[flashxhsx]

for the last part could you just integrate it as ln|x^2+3| or could you not do that since there is a arctan formula for it?

[92JamzC]

Why do you put x=0?

[dhakas]

@92JamzC @92JamzC he puts x=O cause u have to make one factor =o to find out what is the value of the other factor .

he puts x*3-x+6 = A(x*2+3) + (Bx+C)x , if u make x=0 the "C" factor will go O, so u will get the value of the A --> (0)*3-0+6 = A (0)*2+3 ---> 6 /3 = A, so 2=A.-

[buzznix13]

What is there's an irreducible denominator?

[seven0ate0nine]

thanks dude!

[edge766]

the sad part is i think you're too good of a teacher to be a math professor :(

[ydracomagusy]

Long time viewer; first time commenter. These videos are wonderful, and I thought it wouldn't hurt having someone else tell you that.

That being said could I be greedy and ask if you were planning to offer any other upper level math videos. Analysis, ODE, PDE, maybe abstract algebra? You'd have a smaller audience but maybe it would be fun.

Regardless thank you so much. I can attest as a math major and a tutor that I sometimes come back to these for refresher and for notes on tutoring. Thanks

[jkuni]

nice router

[pricesalem]

oh yeah....explanation was great also, clear and concise

[pricesalem]

excellent example, thank you!!

[mrhondacivicsi]

this guy is a god

[Shiro786]

hey patrick i love your long hairy legs!!!

[Anidanka]

hey patrick! got a qustion: what if we had an integral (from 1 to infinity), and a partial fraction (namely: 1/x^2+4x+3)? i assume we do partial fractions stuff, then do the limit where t-> infinity. what I get is divergent to infinity. but from a rule I know if the integral goes from 1 to infinity, then if the power of the denominator is greater than one, the integral is convergent. which one is true? divergent or convergent?

[odinheim]

@Anidanka integral 1/(x^2+4 x+3) dx = 1/2 log(-x-1)-1/2 log(x+3)+constant

[daer3linging]

hey! thanks, do you have an idea how to change this into partial fractions (denominator = [(1-x)^3]*[(2x-1)^2]) ? thanks! :)

[azharmohammed0]

could you explain the last part where 1 over x squared + 3 ( in the second to last line)....why did you put tan there for?? why cant you just ln it?

[xavierkillzone]

Beautiful...

[rapture2100]

your the best !!!!!

thnx alot!  5*

[sullivanseven]

we are the cause of a world that's gone gone wrong, but you are just the opposite.

[ramiosli]

thank you so much

[ramiosli]

thank you sooooo much ...

[MegaJgar]

thank you for saving the trees! thumbs up

[lingojac]

quick question, why isn't the integral of (x/(x^3-3)) just ln|x^3-3|? where did the (1/2) come from?

[thoosah]

When you substitute, you do it this way:

u = x^2 + 3

in next step do derivation of x^2 (that gives you 2x)

that means 2x dx = du => x dx = 1/2 du and you put that 1/2 in front of integral..

[lingojac]

@thoosah i get it now, thanks!

[zonesthesia]

I'm an A student in Calculus and just started watching these videos as a supplement to my text book and lecture. Your straightforward approach really makes it easier to remember everything and I don't have to spend hours a week twitching, hunched over my math book. Thanks!

[lingojac]

thanks for this.  my calculus class consists of my professor in his own world doing math on the chalk board while the class just sits and watches the math fly over our heads, so this video is definitely helpful

[darknecromancer34]

okay I understand now... because the denominatort don't have factor.. ^_^

[darknecromancer34]

uhmm.... I have a question.. why did you put, 'x+3' beside 'B'?

[darknecromancer34]

no, I mean... 'x+C'?, resulting to 'Bx+C'?

[KevinM2012]

That's what you have to do when the denominator is quadratic. The numerator always has an x term that is one power less than the x in the denominator. You just don't see it when the denominator is linear because x^0 = 1.

[DailyReportHQ]

thank you so much. you explain everything so clearly and definitely got me through calculus! keep this up!!!

[cmatthewcrice]

I would like to express my gratitude for all of your hard work in this and all of your other videos.

[Rohan233]

hey umm i would like to know, if a denominator had an x^3 + 5 for example, will you have to add [Ax +B+C] / [x^3+5]?

[patrickJMT]

no, you would factor x^3 + 5 using the sum of perfect cubes formula.

it would factor into the product of a linear factor and an irreducible quadratic factor

[iceboarderz]

I haven't learned the arc tan rule at 5:29 :(

[XCTenSO]

Ummm I'm watching this video right now, and in the first few you steps, you break it down into (A/x)+((Bx+C)/(x^3+3)). In my book, the (Bx+C) is just B (not the same problem)....so why is it (Bx+C)? Thanks!

[iarewanthungry]

I just started this in my college credit calc

[Oblisk47]

You are a god. I don't know why teachers insist on making math so hard when it can be so easy, only if you change your wording around and stop being so traditional. I will be coming back to you for when I get into Calculus. FML

[BlackHatProductionsx]

I agree with you man.

My calc prof makes everything sound as if they are fking hard, and gonna take tons of practice to understand.

[recon455]

Equating of the co-efficients was probably the only thing my teacher didn't cover well. Thanks!

[thekingpoo]

Nice legs... Thank you so much you have helped me trough so many math classes. If I don't understand what the teacher is say and the tutors don't help me, I just hop online and there is Patrick breaking it down step by step. I wish I could pause the teachers and tutors, and then go back a step and repeat it over and over until I get it. Keep up the good work. I hope you keep making videos, because I am going all the way to the 500 + math levels...

[MrPiPPo]

You are a mutha fucking genius man!!! Thanks!

[Lonewolf43]

I have a math midterm tonight and this is one of the problems im having and i kinda get it now. Thank you so much.

[yahbul]

whats this bx +c....can u explain it to me

[kirarei12]

That is what you put over a polynomial that cant be factored further.

[Di3tr1cH]

the degree of the numerator must be one degree lower than the denominator,

so we have 2 cases

constant / linear denominator

linear / quadratic denominator

there's no need to use higher degrees polynomials, because they can be factored to products of linear and quadratic polynomials

this higher grade does not care about the repeated root of the polynomials

1/ (x+2)^2 * (x^2+1)

A/ (x+2) + B/ (x+2)^2 + (Cx+D) / (x^2+1)

[ShadowSlayer5566]

in your video before this on your website (Partial Fractions - How to Determine the Coefficients of a Partial Fraction Decomposition) it was like 30 mins long. You last linear equation you set = to 0 when you had a constant of 3 on the other side. Wouldn't that linear equation = 3

B + 4C + 4D = 0

i think its

B + 4C +4D = 3

not sure though just thought it was a mistake

great vids by the way

[xiaolintraditional90]

thanks for your video, but I'm having some trouble with some more complicated problems.Can you post up more complex problems?

[cabosikeqen]

thanks man

[boxmailman]

thnx a lot, this video and your video lectures are a real lifesaver for me!!!

great job!!

[DoCWaSaBe]

thank you, the other vid u had was a tad confusing, this one is good though!

[osagie]

why did you use bx+c?

[stevenghfc]

because x^2 + 3 is irreducible

[capatilist]

awsome... how about one that incorporates long division?

[calimatlive]

can you post a video with a partial fractions when you need to complete the square? that would be really helpfull

[SkateFL52]

thanks a bunch man.

as a high school freshman, this concept is absolutely infuriating to me. this video helped.

[MICHAELMEMISBACL]

I prefer the method of finding B and C by plugging in A and 1 and -1 into the equation and solving the pair of equations.

[MICHAELMEMISBACL]

Of course the first letter you figure out the value of depends on what happens when you plug in 0 for x.

[kioplo]

why can't you just integrate (-x-1)/(x^2+3) as a whole?...i don't get it, it seems like I could just use u substitution to get 1/u.......

[Pushome]

Hey i've see all your videos and it helped me alot. Can you do a video on polynomials? It will be a great help. Thanks!!!!

[persianpride8004]

For the very last part, instead of doing tan, could you just do u substitution again and get ln (x^2+3)?

[jf3mo]

In order to do ln(x^2+3), you would need to have the form du/u, or the derivative of the denominator present in the numerator. Notice that you don't have that in the las term, as the derivative of the denominator would be 2x and you only have a 1.

[l2attler24556]

For Geeks? So every college student that is having trouble with calc is a geek, by what your saying...

[patrickJMT]

if you care what some schmo on the internet says... you are way worse than just being a geek...

[eddevilfoot]

really your busting patricks chops? he has given you FREE quality calc tutoring at anytime of the day or night with these videos and your given him grief? wow...just wow...

[abcqazqaz]

The only thing i absorbed from that video is that your left handed.

[Neeraj12345678987654]

Hi Patrick

I really enjoy learning from your videos.

I was wondering do you also have to factor the numerator.

like if you had something like 2x+3x+5x^3 in the numerator would that factorize to x(2+3x+5x^2)

Thanks Patrick

[JuggyD18]

are there alot of partial defrac. probs. that you can use "equating the coefficient" ? how limited is it?

[patrickJMT]

u can always use equating coefficients although it can be a bit tedious

[Mike3smith]

in the arctan formula you dont take ( 1/sqr(3) )

you take only ( 1/3) out

isnt that right?

[AcadiaGuitar]

You are a saint. Thanks for the help!