can we do the integral of e^x*ln(x)? Hint: use integration by parts & a special function

Рет қаралды 75,161

5 жыл бұрын

Integral of e^x*ln(x) with special function and DI method (aka integration by parts)
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Пікірлер: 158

@blackpenredpen 5 жыл бұрын

Wikipedia or WolframAlpha?

@ezraguerrero2879 5 жыл бұрын

Wolfram

@user-xq1sl7wy6p 5 жыл бұрын

Wolfram

@veluvoluvenkat7635 5 жыл бұрын

Wikipedia

@thedoublehelix5661 5 жыл бұрын

Wolfram

@mathsvine6032 5 жыл бұрын

Wolfram

@blackpenredpen 5 жыл бұрын

Note. You can also use Ei(x) being the integral from -inf to x of e^t/t I am not really sure why Wikipedia and math world defined it that way. But I have another video on it coming soon

@plaustrarius 5 жыл бұрын

Special functions series perhaps? en.wikipedia.org/wiki/List_of_mathematical_functions

@ansansns1811 5 жыл бұрын

You can turn e^x to a series and then the solution will be very simple

@angelmendez-rivera351 5 жыл бұрын

Ans Ansns Well, no, since you cannot simplify the resulting series into a closed-form answer.

@ansansns1811 5 жыл бұрын

@@angelmendez-rivera351 You are right . The answer isn't a closed form answer but it still a simple solution . Anyone can understand it .

@angelmendez-rivera351 5 жыл бұрын

Ans Ansns You're the only person here who would call that a "simple" answer.

@davedonnie6425 5 жыл бұрын

Old macdonald had a farm Ei(Ei(o))

@blackpenredpen 5 жыл бұрын

Lolllll!!! Love it!!!

@jayapandey2541 5 жыл бұрын

BPRP *doesn't say to try it first* Me: OK. Another non - elementary integral.

@zavionw.8052 5 жыл бұрын

BPRP: *gives a 7-second dark theme to the integral for the intro* Me: Alright another non-elementary integral.

@dhruvshah8310 5 жыл бұрын

Wow !! I've been waiting for this integral for somewhere to be on KZfaq ! And here it is !! Thank you so much sir 🙏🙏😊

@6c15adamsconradwilliam3 5 жыл бұрын

I will never forget the +C

@Honest-King 5 жыл бұрын

I didn't get that grade at any calclus subject but in diffrential I got a +B

@erikkonstas 5 жыл бұрын

Legend has it that the missing ) was never found...

@blackpenredpen 5 жыл бұрын

Oh yea lol!

@Honest-King 5 жыл бұрын

That's what I do when I am bored in math class lol

@tryphonunzouave8384 5 жыл бұрын

@@Honest-King What ? forgetting to close parenthesis ?

@Honest-King 5 жыл бұрын

@@tryphonunzouave8384 Telling the instructer/teacher that he missed a parenthesis

@Extraordinary10s 5 жыл бұрын

I literally spent 20 minutes trying to solve this integral, only to end up knowing that this has a non elementary solution. Is there a way to know whether an integral has an elementary solution or not?

@JSSTyger 5 жыл бұрын

Yes. First write 5 pages of equations and then realize that it doesn't work. That's how you find out.

@General12th 5 жыл бұрын

I do not believe there is any way to know in advance whether or not there exists an elementary antiderivative. You just have to look it up. *Proving* there is no elementary antiderivative is harder.

@mathssolverpoint6059 5 жыл бұрын

Use Laplace transformation

@Honest-King 5 жыл бұрын

@@mathssolverpoint6059 Oh yeah laplace ... I forgot everything eventhough I took it at January - May

@angelmendez-rivera351 5 жыл бұрын

Actually, there is a way. There are algorithms that allow you to test a function for non-elementary antiderivatives. An example is the Risch algorithm, although this one in particular only works for a special class of functions.

@yaleng4597 5 жыл бұрын

"Don't forget the +C" But you forgot to close the bracket.

@blackpenredpen 5 жыл бұрын

Hahahahaha yea....

@VibingMath 5 жыл бұрын

Wow learn something new! Can't wait for your next video on Ei(x)!😍

@jayapandey2541 5 жыл бұрын

Factorial of the Exponential integral. Great idea.

@blackpenredpen 5 жыл бұрын

@@jayapandey2541 Hmmmm, that will be a challenge!

@plaustrarius 5 жыл бұрын

Did u-substitution until I got the integral of 1/(lnx) which cannot be integrated using elementary functions. So my answer turned out to be ln(x)*e^x - Li(e^x) where Li is the logarithmic integral. Fun!

@mehmeteminconkar2590 10 ай бұрын

Me 2

@ezraguerrero2879 5 жыл бұрын

15th view and 10th like. Love being early to watch your content! Always enjoy what you do! I Had barely seen these special integral defined functions; very interesting...

@PokeballmasterInc 5 жыл бұрын

Thanks for answering my question bprp! Glad to finally know the answer now :)

@chankk4560 5 жыл бұрын

is it possible to expand e^x into series form, and make e^x/x into 1/x+SUMMATION(x^(k-1)/k!) from 1 to inf, then we integrate it as power of x?

@angelmendez-rivera351 5 жыл бұрын

Chan KK You can, you simply cannot simplify the answer beyond summation.

@dexter2392 5 жыл бұрын

Yeah, you can integrate it termwise and it turns out to be very pretty (because each term's power will get reduced by 1 because of the /x.) But the thing is, you cannot put it into elementary function form from there. It is still a summation.

@kamilziemian995 5 жыл бұрын

@@dexter2392 Which theorem guarantees that we can integrate this term by term?

@dexter2392 5 жыл бұрын

@@kamilziemian995 well, Taylor's theorem, because polynomials can be differentiated infinitely many times and always give other polynomials, this also means that they can be integrated infinitely many times :)

@kamilziemian995 5 жыл бұрын

@@dexter2392 I remember that doing things "term by term" infinity many times is tricky. Even in "obvious" situation. So, I'm not so sure that this is enough. For example. If I want to compute integral in some limits ("area under curve"), I must guarantying that series converge in appropriate sens, like Lebesgue'a dominate theorem or uniformly convergence. And because there exists functions that have all derivatives, but are not analytical, Taylor's theorem is clearly not enough here. Naive argument would suggest to me, that this is always possible due to Taylor's theorem. Of course I can just don't understand which version of Taylor's theorem you have in mind.

@jirehchoo2151 5 жыл бұрын

Great, I can revise my integration by parts. Thanks! My exam in 2 days time

@anordinarysoul8197 5 жыл бұрын

Learned something new. Cool!

@jjeherrera 4 жыл бұрын

Thinking as a physicist I would just make a Taylor expansion of e^x. Whether the series converges depends on the integration limits.

@wilsonporteus5943 4 жыл бұрын

I don't remember asking for this but I am very grateful

@electrovector7212 5 жыл бұрын

Bprp please show olympiad question solutions. I think it will be very useful. Because calculus is in university or in a little part of high school. But olympiad is based on much simpler maths and it will show everyone to think in other ways. If you notice this I will be very happy. Support please so bprp can see this. Thanks from Turkey

@mustafakemalturak1774 4 жыл бұрын

I enjoying while watching your videos

@frozenmoon998 5 жыл бұрын

Interesting integral!

@MrDerpinati 3 жыл бұрын

i got bored in class and so i challenged myself to this question... i somehow got e^2 ( ln(x) - sum from n to infinity ( (n-1)! / x^n) + C, since i still dont know much about the Ei() function i doubt youll see this since im over a year late but i basically got it from nonstop using the DI method and finding a pattern that could be collapsed into an infinate summation

@dipteshgupta8092 23 күн бұрын

can we solve the integral of e^x/x further by writing the taylor expansion of e^x ??

@yassine321 3 жыл бұрын

The legend say when the exponential enter the integral the integral fall in love with exponential for ever

@mathsvine6032 5 жыл бұрын

Good approach 👍👍

@lythd 5 жыл бұрын

Great video!

@sadigov Жыл бұрын

Very niiiice! I liiiike! - Borat Sagdiyev

@przemysawkwiatkowski2674 5 жыл бұрын

3:40 Why can we use fundamental theorem of calculus? This integral goes from +oo to x... Is +oo allowed here? Why?

@blackpenredpen 5 жыл бұрын

We can be more technical as follows, Break the integral into two piece. One goes from -x to a then the other goes from a to inf.

@mm-ny3nj 5 жыл бұрын

1:13 why dont you use the series definition of thr exponentail function and u will get ∫Σ(x^(n-1)/n!)dx Which evaulates, with interchanging the order of the integral and the summations sign, to: Σ(x^n/(n!*n))+c

@limitXbreaker 5 жыл бұрын

It too me to few months to realise that the channel's name is *Black Pen Red Pen*. I always thought its something blackrependen 😂

@adityasingh4123 2 жыл бұрын

Sir plz concept of exponential intergal fuction pe ekk video bna do i am not clear concept of E(x) I love mathematics plz sir 🙏🙏🙏🙏

@ang_gml 5 жыл бұрын

Amazing!

@IdreesIMala 5 жыл бұрын

Vare good

@deymos_arts6213 Жыл бұрын

Thanks!!❤

@markgh2491 5 жыл бұрын

Day three of asking BPRP to help me solve (3x^3 - x^2 + 2x - 4)/sqrt(x^2 - 3x + 2) dx from 0 to 1. Thank you and keep up the great videos!

@Anistuffs 5 жыл бұрын

I googled that and found this www.quora.com/How-do-I-integrate-dfrac-3x-3-x-2-2x-4-sqrt-x-2-3x-2-dx Hope it helps.

@inkaandinii 3 жыл бұрын

What about if e^x2?

@gabirelsanchezferra336 5 жыл бұрын

=1/x e^x que al integrar = ln|x| e^x +c

@khalafibrahem3928 5 жыл бұрын

please What is the integral of tan (lnx) I need it

@saradehimi4791 5 жыл бұрын

I think I'm not sure : =xtan(Lnx) -2argth(tan(Lnx/2)) +Ln|1-tan(Lnx/2)| + Ln|1+tan(Lnx/2)| + c

@khalafibrahem3928 5 жыл бұрын

@@saradehimi4791 Thank you so much but how you solve that

@saradehimi4791 5 жыл бұрын

Firstly I used integration by parts then I used y=tan(lnx/2) and cos(lnx) =1-y²/1+y² dx=2y/1+y² But as I said I'm not sure brother

@khalafibrahem3928 5 жыл бұрын

Yes that is nice I will try your ways

@ThePharphis 4 жыл бұрын

Great shirt

@rahulchowdhury7635 5 жыл бұрын

u r great

@mdajiruddin8490 5 жыл бұрын

Good

@Culmen222 5 жыл бұрын

Dr. Peyam knows that Ei is german for egg.

@rahulchowdhury7635 5 жыл бұрын

thnx sir

@mathssolverpoint6059 5 жыл бұрын

Use Laplace

@mehmeteminconkar2590 10 ай бұрын

I found a way to write ei(x) as a taylor series expansion

@Honest-King 5 жыл бұрын

I lost my foucs at Ei(X) I don't get it what is " Ei " ? And what does it do ?

@user-sy2vd3kn2x 5 жыл бұрын

Use integration by parts and you wind up with e^xlnx - int(e^x/x). We consider the unsolvable integral of e^x/x as a ei(x). (i think so might be wrong)

@angelmendez-rivera351 5 жыл бұрын

He literally explain it in the video. I still don't understand why people bother to comment on videos without finishing them. It's dumb.

@justabunga1 5 жыл бұрын

Ei(x) stands for exponential integral, which is a non-elementary function.

@chirayu_jain 5 жыл бұрын

Next integral of sin(x)*arcsin(x)

@saradehimi4791 5 жыл бұрын

I think it's : =-arcsinx*cosx +(sinx/√1-x²) -2Ln|tan(x/2)| +Ln|tan²(x/2)| + c

@chirayu_jain 5 жыл бұрын

Saya Sayya but how?

@56shauryasingh33 5 жыл бұрын

@@chirayu_jain its basic product rule of integration

@chirayu_jain 5 жыл бұрын

JustArduinoThings Ok 👍🏻 understood

@56shauryasingh33 4 жыл бұрын

@@aneeshsrinivas9366 where did you study maths?

@future62 5 жыл бұрын

Deus Ei(x) Machina....

@aleksandervadla4840 5 жыл бұрын

Do you have any tips to Get better in meth?

@sadigov Жыл бұрын

Don’t do meth!

@sriramshenoy3454 5 жыл бұрын

Can you integrate lnx/(1+lnx)^2? Thank you

@blackpenredpen 5 жыл бұрын

Sriram Shenoy Where did you get that problem?

@sriramshenoy3454 5 жыл бұрын

@@blackpenredpen My teacher gave it to me

@justabunga1 5 жыл бұрын

The answer is x/(1+ln(x))+C.

@mhersaribekyan1487 5 жыл бұрын

What if it is -C and not +C ? r/hmmm

@user-zy6gn8vz2x 5 жыл бұрын

C might be negative as well as positive as well as zero. We'll never know 'cause of the undetermined form of the integral

@justabunga1 5 жыл бұрын

The C stands for the constant of integration. Even if you put in negative numbers or 0, it would count as +C.

@mhersaribekyan1487 5 жыл бұрын

@@justabunga1 Thanks for explanation, but it was just a joke!

@titanwilkins4044 5 жыл бұрын

MATH YES

@nuklearboysymbiote 5 жыл бұрын

What is the meaning of math?

@breadsneakypeaky1104 5 жыл бұрын

To be able to get a gf

@artey6671 5 жыл бұрын

Having fun and being the cool kid in class.

@erikkonstas 5 жыл бұрын

To flunk hilariously.

@paramgupta7835 5 жыл бұрын

42....+1

@okhtayghorbani6361 5 жыл бұрын

👍🏻👍🏻👍🏻🙏🏻

@bikrammarasini2021 5 жыл бұрын

Please integrate xtanx

@justabunga1 5 жыл бұрын

The integral is non-elementary. It would come out to be -xln(abs(cos(x)))+integral of ln(abs(cos(x))dx+C

@JivrajSandhu 4 жыл бұрын

I'd like to report a blue pen also sneaked into your video

@user-rz3id7nm6s 5 жыл бұрын

Don't forget +c 😂😅😅😂😃

@acertainbastard5579 5 жыл бұрын

Or is it -C?

@user-rz3id7nm6s 5 жыл бұрын

@@acertainbastard5579 The same thing

@acertainbastard5579 5 жыл бұрын

@@user-rz3id7nm6s that's like saying C++ is the same as C

@user-rz3id7nm6s 5 жыл бұрын

@@acertainbastard5579 My friend . I meant +c it's just like -c

@acertainbastard5579 5 жыл бұрын

@@user-rz3id7nm6s and I'm saying C++=/=C Both are separate languages

@fabiotiburzi 5 жыл бұрын

tacci tua!

@pichass9337 5 жыл бұрын

Yuh