Weierstraß substitution: strange, overpowered and very hard to pronounce

The Weierstrass (can't even pronounce it in my head while writing it😂) is quite useful when you encounter integrals involving rational expressions of trig functions. I hope you like the video and forgive me for my horrible pronunciation as well as introduction of epsilon😂

[leesweets]

a^n + b^n = c^n has no integer solutions for n>2. This shall be left as an exercise to the watcher.

[ahsgdf]

Great again. Thank you.
How to pronounce Weierstrass? Try Viashtruss, in the end short like the first name Russ.

[holyshit]

Weierstraß substitution is somehow connected with Euler substitustion
By Pytharorean identity we know that cos^2(x)+sin^2(x)=1
so cos^2(x)=1-sin^2(x)
If x is in first quadrant we can write
cos(x)=sqrt(1-sin^2(x))
Now we can use Euler's substiutution to get
sqrt(1-sin^2(x))=(1-sin(x)) t
so
cos(x) = (1 - sin(x)) t

[zunaidparker]

The first problem took way too many steps until multiplying by 1-phi^2 in numerator and denominator (should have been done straight away to avoid all the remaining common denominator manipulations).
The second problem skipped way too many steps during the (pi/2-eps) substitution and didn't explain how the limits of integration swap around but then are negated by the minus sign that you pick up in the differential.

[RealTechTV]

hello professor. where i can get the black board app that you using? please help me.
thank you.

[RealTechTV]

Hello, what is the name of the application your using? Is it available on the play store?
I’m looking for a scrollable black board

[matteocilla]

Is there a result about integrals that says an integral can only be solved by one method? Or are there always several ways of solving an integral?

[thomasblackwell]

Great video as usual but how about using chi next time.

[emanuellandeholm]

It's pronounced something like vahy-er-shtrahs. IPA = ˈvaɪ ərˌʃtrɑs. I think you nailed it!