The solution to non elementary integrals is to create a new function for every new non elementary, call it “peepeepoopoo(x)”, add a “+C”, and call it a day 😎
If you continue algebra video series I would like to see eigenvectors case when there are less eigenvectors than eigenvalues ,similar matrices , Cayley-Hamilton theorem , orthogonalization , reflector matrices , rotation matrices
Bro you literally came in dream 😭😭😭😭(I have no idea how much I have been watching your channel that you are coming in my dreams) and I saw that you had changed your channel name and I was crying haha
Could you please clearify when could we use "or change to" complex numbers when doing integral? + How could we use the result to find something like experimental values on the complex plane
Can this be solved using the lambert W function instead? I can see that if take y = x^2*(e^(x^2)) then W(y) = W(x^2*(e^(x^2))) => W(y) = x^2 idk how to go about from there
Euler's reflection formula gets them in terms of each other. Then you'd want to use other ways of isolating them using other functions, like the integral representation of the Riemann Zeta function, or the Ramanujan Master Theorem.
Nice try Newton. But you still have to study. Let me note that erfi(x) is ultimately a real increasing function for real values x>0. So I can easily prove that the final formula is wrong. Maybe, just maybe it should be a + instead of a minus. I think I caught the moment when you messed up. That was an improper shortening of integrals and differentials. d/dx(integral (f(ix)))=f(ix)/i. Proof: x^2e^(x^2) > 0.5e^x^2 - C*erfi(x) for x>1 and C
M=xe^x²+(1/2×e^x²)-(1/2e^x²) =1/2×[xe^x²]-e^x² For e^x² Let s u'=1 and v =e^x² u=x and v'=2x×e^x² e^x²=[xe^x²]-2x²e^x² =[xe^x²]-2M Finally M=1/2×[xe^x²]-[xe^x²]+2M M=1/2×[xe^x²]
Do not use the times sign in algebra/calculus. Use an asterisk or have, for instance, (1/2) right up against the exponential function or right up against a bracketed expression. For clarity/emphasis, your fractions should have grouping symbols around them.
Pfft, 0 marks, forgot the +c Edit: actually since the error function is itself an integrand, couldn't you say that the constant is part of the error function?
Outstanding presentation
Best regards from Brazil
Nothing imaginary about how good a teacher Prime Newtons is. The only error is to not watch his videos! 😊
That was good 😂
4:21 you can also try to differentiate the main function e^(x^2) and see by chain rule that there will be 2x and integrate by inspection
The solution to non elementary integrals is to create a new function for every new non elementary, call it “peepeepoopoo(x)”, add a “+C”, and call it a day 😎
If you continue algebra video series I would like to see
eigenvectors case when there are less eigenvectors than eigenvalues ,similar matrices , Cayley-Hamilton theorem , orthogonalization , reflector matrices , rotation matrices
Bro you literally came in dream 😭😭😭😭(I have no idea how much I have been watching your channel that you are coming in my dreams) and I saw that you had changed your channel name and I was crying haha
Thank you very much sr for this wonderful insights on impossible calculus questions more especially on error functions
Those who stop learning... stop living...
Amazing how you explain all
Greetings
Love your channel
Very clear presentation!
Amazing math horizon. By the way, where this math knowledge is applied in real world. If this comment is added, the lecture will be more excellent😂😊
Thank you Sir! Your videos are so educational.
Sweet! Now, all you need to do is show some examples that use the Erf(x) and the Erfi(x).
Isn’t that the same as integrating W(x^2) ?
No, W is the inverse. W(x²) is to arcsin(x²), as x²e^(x²) is to sin(x²).
Very good. Thanks
Nice job
That's sick
Could you please clearify when could we use "or change to" complex numbers when doing integral? + How could we use the result to find something like experimental values on the complex plane
Since the integrand is x^2 exp(x^2), could we use the Lambert W function ie W(x^2) . Isn't there a known form for the integral of W() ?
Can this be solved using the lambert W function instead? I can see that if take y = x^2*(e^(x^2)) then W(y) = W(x^2*(e^(x^2)))
=> W(y) = x^2 idk how to go about from there
Is there any numerical method available to calculate gamma function of non analytical numbers like (1/3), (1/5) ?
Euler's reflection formula gets them in terms of each other. Then you'd want to use other ways of isolating them using other functions, like the integral representation of the Riemann Zeta function, or the Ramanujan Master Theorem.
Why cant x be real if there is no monis in the exponent?
Sir I really need your help
Wow🇮🇹
Bro Learn sppu m2 error funtion
Nice try Newton. But you still have to study. Let me note that erfi(x) is ultimately a real increasing function for real values x>0. So I can easily prove that the final formula is wrong. Maybe, just maybe it should be a + instead of a minus. I think I caught the moment when you messed up. That was an improper shortening of integrals and differentials. d/dx(integral (f(ix)))=f(ix)/i. Proof:
x^2e^(x^2) > 0.5e^x^2 - C*erfi(x) for x>1 and C
it doesn’t take long to just open wolframalpha and check the answer lol
ok
🤓🤓🤓🤓
M=xe^x²+(1/2×e^x²)-(1/2e^x²) =1/2×[xe^x²]-e^x²
For e^x²
Let s u'=1 and v =e^x²
u=x and v'=2x×e^x²
e^x²=[xe^x²]-2x²e^x²
=[xe^x²]-2M
Finally M=1/2×[xe^x²]-[xe^x²]+2M
M=1/2×[xe^x²]
Do not use the times sign in algebra/calculus. Use an asterisk or have, for instance, (1/2) right up against the exponential function or right up against a bracketed expression. For clarity/emphasis, your fractions should have grouping symbols around them.
Thanks so much for the explanation
u•v - ∫ u'•v' => ∫ x^2•e^x^2 •dx
u=x^2; u'=2x; v=e^x^2; v'=2xe^x^2
x^2•e^x^2 - ∫ 2x•2xe^x^2
x^2•e^x^2 -(2x^2/2 • 2xe^x^3/3)•dx
x^2•e^x^2 -(6x^2 • 6xe^x^3)÷6•dx
x^2•e^x^2 -x^2•xe^x^3 •dx =
e^x^2 -e^[(x^3)+1] •dx
e^x^2 - e^[(x^3)+1] •dx |•-1
1,71828 = e-1 e^x^2 - e^[(x^3)+1]
[-e+1•dx] => ∫ [-1,718 •dx]
Pfft, 0 marks, forgot the +c
Edit: actually since the error function is itself an integrand, couldn't you say that the constant is part of the error function?
And now differentiate this... 😂😂😂
First like ,edited and comment q❤❤❤❤❤
When you take this rough integral on a test correctly, but forget +C, and bet zero points💀☠