Відео

asnwer=(x+1)(x-1)

Which app is this please tell me

Thank you! The steps are really clear! I noticed where I was doing wrong and what was getting me the wrong answer 😅

hi rebecca. great job.

Awesome video!!! I love your way of writing, it's super clear and nice to look at

Thank you so much for solving the question. It helps a lot..❤

English captions ? 😅

👏🏻👏🏻

Solution: ∫ln²(x)/x*dx = ------------------------------------ 1st solution by partial integration: Partial integration can be derived from the product rule of differential calculus. The product rule of differential calculus states: (u*v)’ = u’*v+u*v’ |-u’*v ⟹ (u*v)’-u’*v = u*v’ ⟹ u*v’ = (u*v)’-u’*v |∫() ⟹ ∫u*v’*dx = u*v-∫u’*v*dx ------------------------------------ ∫ln²(x)*1/x*dx = ln³(x)-∫2*ln(x)*1/x*ln(x)*dx = ln³(x)-2*∫ln²(x)*1/x*dx |+2*∫ln²(x)*1/x*dx ⟹ 3*∫ln²(x)*1/x*dx = ln³(x)+C |/3 ⟹ ∫ln²(x)*1/x*dx = ∫ln²(x)/x*dx = ln³(x)/3+C/3 ------------------------------ 2nd solution by substitution: u = ln(x) du = 1/x*dx ------------------------------ = ∫u²*du = u³/3+C = ln³(x)/3+C Checking the result by deriving: [ln³(x)/3+C]’ = ln²(x)/x everything okay!

this is not even worth solving, it is a direct ∫ln(x)dx = x ln x - x + x also valid for linear of x but divide by the coefficient of x

Let v = x + 1, dv = dx I = (x + 1)ln(x + 1) - ∫(x + 1)/(x + 1)dx = (x + 1)ln(x + 1) - x + c

Can you just divide top and bottom by t+1 like that? Doesn't t+1 have the potential to equal zero? So the integral wouldn't be proved to be correct for t = -1 right?

Why not √4=-2 also?

Nice video

Clear explanation 👏

very good explanation

¼Log |x⁴-5| +C

Please upload in English we are unable to understand please Mam

thank you my late night brain couldn't figure out why it was -pi/2. the graphs really helped

God bless you. You explain very good.

❤❤

I heard your answers. I enjoyed very much your explanations.you explain verh good.❤

you can also multiply both the numerator and denominator by 1/x^3 and simplify before taking the limit

Yes, L’Hopital in a jiffy. Because the initial equation is already in the infinity/infinity form. First derivative for both.

Actually,it is great work so to be continue to others videos

Thank you so much, this saved my exam

can you explain how to get the h(h-6)/h???

homelander here: where is my son?

can you explain the MIT integration 2024 competition (finale) because it's beyond my understanding

you're a genius, i tested by substituting the value of x to 10,000 integer and its came close to value of -2 , so basically any limits related to infinity, with any variables will only involve the power degree of the D and N from the expression, and other constants can be omitted, pure genius :) i love it

Trick: ∫x²√(1 - x²)dx = (ax³ + bx)√(1 - x²) + c∫1/√(1 - x²)dx Differentiate both sides wrt x and equate coefficients.

damn😬

What is the whiteboard?

Took me 2 seconds lol. Nice video

Thanks for sharing this!

Which country

its very easy problem this problem is solved by studdents of 10 11th class in india we can solve this by differentiation also 1st comment please pin my comment

Thank you for your videos!

Integration(xsin10x dx)=1/100*integration(10x * sin10x d(10x))=-1/100* integration(10x d(cos10x)) = -1/100 * 10x * cos10x + 1/100 * integration(cos10x d (10x)) = -1/10 x* cos10x - 1/100 * sin10x

Thanks

You don't prove you can switch lim and ln. Besides, it's obvious that using ln you'll get an e somehow...

Why do you put 5 in the integral?

Thank you bery muchh.❤❤

Merci beaucoup 😚😚😚

I tried it this way: tan(2x)/x.(1/2).(2/1)=2*tan(2x)/2x=(2*(sin(2x)/cos(2x))/2x=(2*sin(2x))/2x*cos(2x)=2*(sin(2x)/2x)*(1/cos(2x))=2*1*1=2

... A clear presentation on an indeterminate limit form ... just an accidental small spelling error at the beginning ... 'indeterminate' instead of 'inderminate', but of course you know this Rebecca ... thanks and best wishes, Jan-W

This is a circular proof . You can't use natural logarithm in the proof. The very defination of a natural logarithm is it's a logarithm with base e

The Exponential Function e^x is realised from a binomial in two variables and has nothing to do with limit theory: ua-cam.com/video/J3itUB3wGmQ/v-deo.html

You didn't justify that you can switch the order of ln and lim

to prove the series of ln(1+x), you do need the derivative of ln(x) already but it's proof already requires knowing this limit is e