The best way to do partial fractions (is to NOT do partial fraction)
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- čas přidán 8. 11. 2021
- The best way to do partial fractions is NOT to do partial fractions. Learn how we can do the integral of x^2/(x^4-1) and the integral of 1/(x^4-x) without doing the "traditional partial fraction decomposition". Here's the setup for the usual way to do partial fractions: • Ultimate Partial Fract...
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¨The best way to do partial fractions is not to do partial fractions¨
A very smart man
any partial fraction problem can be done by multiplying the top and bottom by a specific expression (but it’s very hard to find the expression without knowing the solution)
You know, sometimes integration just looks like a magic trick.
STRANGE GAME. THE ONLY WAY TO WIN IS NOT TO PLAY.
Stop yelling your post in all caps.
@@robertveith6383 In 1983 there was little choice.
@@robertveith6383 it’s a reference
The well chosen 1 and 0, my favorite algebra trick.
Feels good when you get both the questions right without seeing the solution with a different approach.
Ok I admit my approach with the first one was almost same. Good video :)
My maths teacher says the same, too!
Bprp is ur math teacher
@@jrbros2371 the plot twist. 🤣🤣
When someone uses 100% of their brain:
No, 100% + 10% - 10% of their brain.
@@davidbrisbane7206 400% of 25% of their brain
The sound of the your marker pen (who it fell down) is just as enjoyable as the sound of the Shell in the matrix movie to me; because I love both of you (Matrix and bprp)
I actually love you, thank you
You really blew my mind!
Wow that is so helpful!🔥
No way 😂😂... You made it so simple .. you are actually re-writing history!!... Thank you Sensei!!
Just wow. Thank you so much for this. Now I can solved DE equations with partial fractions without being afraid that I might not finish the exam.
Already knew this,, GB sir taught this in his class.!
Yay I was able to guess that a hyperbolic function was involved!!!! I had also guessed that it was inverse tangent hyperbolic!
I’ve never learned about hyperbolics, could you please make a video on them???
Oké Einstein
I haven't learnt what those are but got the solutions using some algebraic manipulations. This is why integration is fun.
I love you teacher, that's it.
As someone who hates partial fractions I appreciate so much this video.
I like this video 100% - 10% + 10%
The answer to the first one is only defined between x=-1 and x=1 no? Would be interesting to see the solutions outside this bound, they will of course be independant of each other but still
so smooth ngl
Nicee work
If you hold that pokemon then you can solve any difficult problem in Calculus .That Pokemon is giving him much power to solve any math problem.
This is pure beauty when an established method can be avoided by just doing algebraic stuff to make the expression go easier to calculate.
Hyperbolic trig functions weren’t covered very much in my Calc 1 and 2 classes (currently in Calc 2, textbook is ETF 7e, just got done with improper integrals and partial fractions). I think I’ll just stick with partial fractions
Hyperbolic functions are really both fun and useful. E. g. you can also do integrals with square roots of (1+x²) by using the substitution x = sinh(u).
For me, everything in math is cool until some trigonometry functions decide to get involved.
Clean af
Can i do something else to the first one without adding Hyperbolic Function? And no partial function
You could repeat the trick: 1/(x²-1) = 1/2 2/(x+1)(x-1) = 1/2 ( (x+1) - (x-1) ) / (x+1)(x-1) = 1/2 ( 1/(x-1) - 1/(x+1) ).
Which obviously gives the same result as a PFD.
The second one got me shook LMAO
I always do this😁😁
So cool
Just for fun... Could you do the integral of (x^2+1)^2/(1+x^6)dx in thirty seconds? V:
Use wolfram lol
Nel primo esercizio perché si mette arcthx e non arcctghx negli integrali indefiniti?
perché l'integrale noto risulta nell'arcotangente ahahah
Cool. Your skill improved with your beard.
I may be wrong but how can u in the second problem be negative? I thought 1 - 1/(x^3) is always positive.
Try a few values and see. Let’s try x=0.5.
(0.5)^3 = 0.125 = 1/8
1 - 1/((0.5)^3) = 1 - 8 = -7
So, it’s not always positive. :-D
Well, if 0 < x ≤ 1, then 1/x³ ≥ 1
and 1 - 1/x³ ≤ 0
u can be negative When x is between 0 and 1, just plug some numbers and You Will see.
مذهل
This is so funny I did it I agree with Daoism.
You should always try to make life as easy as you can.
Wolfram alpha every time.
But for except time consuming i dont think there is any problem with partial fractions.. but this is cool!!!😂
The best way to do calculus is by not doing it the way the textbook says and by doing it the right way
But I like doing them , they’re fun
It depends in the particular sum right?
It always better to seperate up polynomials in an integral before wrestling with it 😂😂
The problem of this methods is to see the trick. They demand some creativity.
Love watching ypur videos, however I think you were wrong on the first integral. I checked it using an online integral calculator and the result was -ln(abs(x+1))/4+arctan(x)/2+ln(abs(x-1))/4
I know why: integral of 1/(x^2-1) is not arctangent but it is a natural logarithm. You can check it yourself it is a formula.
@Pol Patrol Surely it can be both. The hyperbolic functions are defined in terms of e^x.
Here’s a homework for you: plot your result and plot the video’s result. If they only differ by a constant they are both correct
It is the same answer. Look up how inverse hyperbolic tangent is defined.
@@polpatrol5215 bruh
Yiu really look like Sun Tzu or some wise sage guy because of that beard
blue pen is not allowed in bprp world
:D
:D
Some smart people can teach.. some can't.
😍😍
Holy f...
what the frick
… is to just use your pc
Sir I want to talk to you for a while. How can I do so? Is there any email ID or Instagram profile?
But you are still doing partial