integral battle#8: division or multiplication?
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- Опубликовано: 2 окт 2024
- learn the DI method: • integration by parts, ...
integral of e^sqrt(x)/sqrt(x) vs. integral of sqrt(x)*e^sqrt(x)
integral of e^sqrt(x)/sqrt(x), integral of sqrt(x)*e^sqrt(x),
integral by substitution, integral by substitution and integration by parts
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blackpenredpen
You should factor out the 2e^u at the end to make it neater.
I'm sure you know this but also for integration by parts there's a pneumonic LIATE (logs, inverse, algebraic, trig, exponential) if it comes first you do the derivative of those
Ben Shiffman *mnemonic
It's ILATE
Ben Shiffman lol I learned it as LIPET (logarithmic, inverse trig, polynomial, exponential, trig)
Wow the left one was part of a problem on my calculus II test!
Christian Rodriguez how did u do?
blackpenredpen Well it was mainly on infinite series and all that jazz, which I'm a bit shaky on, but nevertheless I passed with the second highest grade in the class :D and of course I got full credit on all of the integration questions thanks to your videos 😄
Christian Rodriguez oh wow. So glad to hear and great job! :)
blackpenredpen thank you! Keep it up with the great videos!
Christian Rodriguez thanks and will do!
THE U WORLD!
Your videos are amazing 👍
Maher Hawari great. I am glad u like them
for the second integral i was screaming Lambert W function, then i realised idk how to integrate it 😂
u can solve sqrt(tanx) using (tanx+cotx)=i and (tanx-cotx)=-i . the integral of tanx is simply the arithmetic mean of those two integrals
Integral on LHS by substitution
Integral on RHS by parts
I (for once) got a question right!
I have done both by myself.... Give me a like
What if... You can turn the second integral into a part of the first integral. Just multiplying top and bottom by sqrt(x) will leave us with the integrand x•e^(sqrt(x))/sqrt(x).
Can You Please Please Solve integeral of x⁴/(x⁴-1)²
Nice🌹
Sir can u suggest me a book containing only integration problems a advanced one
Just look them up online. If you want really hard ones take some from the putnam or putnam practice twsts and the like
3^x=0 what is x and can we make a revulation in math with this x number like in 1600s year with imaginary numbers.And it can be any number to some power that will equal to zero
3^x = 0
xln(3) = ln(0)
ln(0) is negative infinity, therefore x must equal negative infinity. This is a documented number and will not make any kind of "revulation"
There is no real solution to 3^x = 0, since -infinity is not a number.
If you asked the question "What is the limit as x approaches -infinity of 3^x", then the answer would be 0. But you never actually get there.
Because a^(-b) = 1/a^b you know x is going to be a big negative so this is a differwnt case where x approaches -infinity but there is no definition for x, but we csn take the limit. This is differnet from the sqrt (-1), where there is no way to express that in limits and was a completely different senario.
Shouldn’t u^2 = |x| ? Why not?
U^2 will always be positive.
can you do
integral of x^x
vs
integral of sqrt(tan(x))
??
+Anton Kulikov integral of sqrt(tan(x)) can be solve because we can draw the graph of the function that means we can measure the area blow the graph
i still think that integral of sqrt(tan(x)) is a nightmare...
blackpenredpen The result is, but the method is not bad.
And did anyone have a solution for x^x ?
@@italophile2437 This is a non-elementary integral.
I have to admit, I hate, hate, HATE, the D-I method. It's way easier to digest using classic integral(u dv) = uv - integral(v du)
i donot understand it because i am 4th grade that is for grade 8
no no no, that is for 11-12th grade, but you can learn it in 4th like I learn it in 5th grade!