fun integral battle#4: rethink factoring...

integral of 1/(x^4+x) vs. integral of 1/(x^2*(x^4+1)^(3/4)),
(Sorry, this is a re-upload since I had a typo in the previous upload)
MIT integral bee 2006: • MIT 2006 Integration Bee
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blackpenredpen
tags: integral of 1/(x^4+x), integral of 1/(x^2*(x^4+1)^(3/4)), integral battle, fun integral problem, MIT integral bee problem, integralcalc, integral calculus, calculus 2, calculus 1 integral, challenging integral problem, how to do substitution for integral, u-sub examples, integral examples, steve chow,

[@AsafShahar]

This is just ingenious
.

[@blackpenredpen]

Asaf Shahar thank you

[@diegomontalvo9173]

It would be great if you make a video explaining hyperbolic trigonometric functions.

[@Ghost____Rider]

I did substitution of tanθ=x^3/2 but your way is much nicer. Great video ;)
*Edit: For the first integral that is*

[@clusteralgebra]

Another way to do the first one: 1/(x^4 + x) = 1/x(x^3 + 1) = 1/x - x^2/(1+x^3) and antiderivative is just ln x - ln(1 + x^3) / 3 + C

[@tychophotiou6962]

Alan Yan that's exactly how I did it as soon as I saw it.

[@rob_dyy]

I watch your videos all the time and learning so much more than what the cal class offers, Great video.

[@blackpenredpen]

I am very glad to hear about this!
And I plan to make more of this kind of integral videos. I think it's a really good way to really learn the integration techniques and more fun too!

[@damirbajramovic292]

Dude, I stopped watching South Park for fun and started doing integrals. You rock!

[@dalek1099]

This sort of thing reminds me of some other methods that often tutors seem to not know when approaching what can be very easy integrals like integral xsqrt(1+x) dx doesn't have to be by parts instead write x=x+1-1

[@theessentialist6813]

Wow!Great videos,great explaining and great examples!Thank you so much!
Also I have some integrals examples which I am dealing with lately and I am having some diffuculties to deal with!Would u be able to have a look to them and help me with?
THANK YOU SO MUCH!

[@alecambrose151]

This is art

[@shankargore9084]

solve integration (x^2+1)(x^2+2)/(x^2+3)/(x^2+4)

[@blackpenredpen]

good problem, maybe i will out it out in a vid one day

[@diamonddave2622]

1/3 (3x - 9 tan^-1 (x/2) + 2 sqr3 tan^-1( x/sqr3)) + C

[@integrationbee2511]

Visit our channel to find great integrals.

[@ernestschoenmakers8181]

Correct, i had the same answer.

[@thisismycoolnickname]

I did the first one by adding and subtracting x^3 in the numerator
1dx / x(x^3+1) = (x^3+1-x^3)dx / x(x^3+1)
So I got a sum of two integrals and the answer I got is ln |x| - 1/3 ln | x^3+1 |, and it's equivalent to yours :)

[@ernestschoenmakers8181]

Well i came to the same answer but i used the method of partial fraction decomposition and did the integrals subsequently. This method needed a lot more work than yours.

[@sagarmajumder7806]

I take my words.You are not only good mind manupulation, you are "PRO" at this🤯🤯🤯😎😎.I felt sorry bcoz I have shortage of words tp explain it.

[@funmomentmemes]

How to do this math
integrate
(1-v/v२+v+1 ) =1/x dv/dx

[@albertomaximilianovenegasl6880]

but the fourth root of x raised to the fourth is x only if x is greater than or equal to zero, otherwise it would be -x .... I have that doubt, then we would have to make two different integrals, one assuming that x is positive and the other where the x is negative?
help me please!!! PD:
excuse my english but i speak spanish

[@magepker728]

wow i solve this using trig sub which took me 1 page.. and this method of yours is extremely useful and easy. have you come up with a name for this method yet?? heheh

[@yanquoimolubah1507]

Do you always have to make calculus this easy 😂😂😂😂

[@_TharunKumar]

These type of integrals simply solved by taking x power in common

[@proofofalifetime488]

Thanks for making all these awesome math videos for us math people around the world! :)

[@shamilbabayev8405]

1/(x^4+x)=1/x-x^2/(x^3+1) , the rest of steps are clear.....

[@jackkalver4644]

You forgot to multiply the integral by sign(x).

[@alessandrofaranca1309]

i did the first with the separate fractions method and then using the exact approach showed for the second one.

[@amanmahendroo1784]

what if we do tan substitution on No2?

[@assaultrifle6221]

1/(x^8 + 1) ?????????

[@zhahrotunnisa7577]

thank you. this video is good

[@belmokhtarbentadj9794]

great work i love it

[@integrationbee2511]

Visit our channel to find great integrals.

[@buenchiko007]

wow, i never knew there was such a way to solve an integral, thanks for sharing!

[@blackpenredpen]

Yea, this only works for special occasions

[@integrationbee2511]

Visit our channel to find great integrals.

[@holyshit922]

Integrating of binomial differentials
In polish and russian schools there is standard substitution for this

[@CheapPhysics]

I have made both of them maaan!!!!

[@TonySoprano1729]

es interesante que la forma en que resuelves la primera te simplifica bastante, yo lo primero que pensé fue por fracciones parciales y si llegue a un resultado equivalente al tuyo, pero por parciales es más largo el procedimiento, en fin excelente vídeo saludos.

[@juandeluna2652]

Excellents tutorials, I've learned more and more, practice and love for maths, two essential things, thanks for all your wonderful posts.

[@tylerwebb7303]

How can you factor out an x^4 power in the denominator of the second integral if the quantity you are factoring it out of is raised to a power?

[@x-warrior8517]

In india ,we call it 'kutur putur ' method.thanks 😍

[@gatoquellora3201]

Eres el puto amo!!

[@carlosv.ramirezibanez3305]

Para la primera integral sume un cero: 4x^3-4x^3 y sale directo

[@albiceleste101]

that was actually fun! specially because I didnt have to solve them

[@srpenguinbr]

in the first one, I factored out x^2 and made two subs. It worked

[@がつかくん]

wow!I got it... I had no idea there was such a way!thank u.

[@yoursmartypie1038]

The video was very helpful.
Thanks

[@ilaganpaulvincentr.4282]

Mind blowing strat! Thank u ❤

[@ColeHudsonRocks]

This is maybe my favorite youtube channel. I love the way you approach the different problems. It teaches me not only how to solve the problem, but also how to approach other problems. Thank you! 谢谢！

[@blackpenredpen]

Cole Hudson thank you!

[@corderorosalesjulia9496]

Te amo :)

[@w_wahlang1990]

why not split 1st one as 1/x - x^2/(1+x^3) but answer is different from yours.

[@reIONEre]

wadbor wahlang lnx-ln(1+x^3)/3= (ln(x^3)-ln(1+x^3))/3 = -ln((1+x^3)/x^3)/3 = -ln(1+x^-3)/3; as you can see, both answers are the same.

[@radouaniabdelhadi332]

Very nice

[@remyassier1758]

Great !!

[@abasiomary9609]

Genius

[@00Goodwin00]

At 8:33 the divided by 3 has vanished. Great way to do it took me a while doing it the partial fractions way.

[@blackpenredpen]

Alex Goodwin I see. I will have to edit that out

[@MarceloRodrigues-kl6cz]

Never would i think so.

[@andreshippy17100]

excelente, saludos desde Colombia

dude, your mic is just ridiculous

[@omereng2827]

thanku very good way

[@tanvirsaikat602]

great man...u r the boss

[@farooq8fox]

Easy 👌

[@Humongastone]

what does he mean @1:20?

[@yhonsalas9692]

(1+x^3)

[@MegaBuwaneka]

Great piece of work

[@mazharbiplob2714]

please solve that...... dx/x^2(x^2+1)^2

[@ernestschoenmakers8181]

You can solve this integral 2 ways: trig sub and partial fractions, try both, by the 2nd one you need integration by parts.

[@MegaEsaka]

Nice teaching :)

[@koashaygyi]

Thank you.

[@koashaygyi]

Thank you.

[@sunillokhande3009]

Sir plese integrate 1/(x^7+ 1)

[@ernestschoenmakers8181]

Well this integral can be done by complex numbers.

[@faridhamel9334]

Thank you.

[@KN-jq2hi]

Thank you :)

[@anasselahmadi5503]

Thanks for thes vedio: )

[@blackpenredpen]

You're welcome. I am glad that you like them!

[@iZenZation]

genius

[@blackpenredpen]

thanks!

[@yhonsalas9692]

(x^-3 + 1) ???? negative -3

[@malukoandmigga]

pinche nonito donaire

[@blackpenredpen]

?