how to integrate using u substitution

Understand u-substitution, essential examples,
integral of sec(2x)tan(2x), @0:30
integral of sec^2x*tan^2x, @3:57
integral of sin(x)/(1+cos(x)), @8:07
integral of sin(x)/(1+cos^2x), @16:53
integral of x*sqrt(x^2-1), @23:22
integral of x*sqrt(x-1), @27:00

[sciartion]

You make calculus a lot easier :')

[scitwi]

15:29 You could get rid of that minus sign by swapping the limits of integration.
This reverses the area into its negative, which would then cancel with the minus sign ;)
That would lead to less noise with the minus signs afterwards ;J
21:15 Same here.

[gennadiymostovskiy]

Finals are coming up and i spent three days trying to understand this stuff. After watching this video, i have been knocking out every integral they threw at me. You're the man!!!! Thank you!

[orwxll]

This is by far the best explanation outside of visiting my professor during office hours that I’ve ever seen apropos this topic. Thank you for this wonderful video!

[aronpacino]

5:15

sec(x) is not a good choice for you

Okay, noted, thank you for reminding me because i might choose sec(x) soon in my life

[juanrobles]

You are very enthusiastic and helpful. Thank you for making this easier to many students worldwide.

[nintendude]

This man is just casually wearing a supreme shirt.

[karolinapadillavaldez]

Thank you so much for this! You make it so easier and funny, greattings from México :D

[jondoe-nf]

So goated. I have my AP Calc exam in 2 days and I forgot all this but now I'm good to go. Thank you.

[ElRenoto]

Loved your videos, great channel ! Congratulations

[jamesthumm]

dude you just saved me a quiz grade thank you so much

[nooraanwahi]

Thaaaank you your method really makes sense to me, when I learned at the classroom I was confused but now I can solve

[dengalekemiker]

Never heard of sec(x) before this channel.

[tchue]

Really helpful. Thank you & keep up the good work!

[dhairyasomani]

That's the best man hats of to you,
thanks a lot bro!!!

[wenhanzhou]

I think I have single-handedly learned calc1+ lv math just by watching your videos.
PS: My class just started with derivative.

[anishasaumyaroll]

thank you so much for your amazing teaching style...it really helped me understand it in a much better way . also now I am able to solve questions much much faster .you are awesome sir

[muazalli]

man i wish you were my calc teacher (i love my current calc teacher but you're also amazing)

[bonbonpony]

10:50 The first integrand is just `tan(x/2)` though (remember the half-angle formulae for tangents?).
So maybe this fact can be used here somehow?
Also, I find it kinda interesting that integrating the tangent on a quarter-circle can give us `ln(2)` :>

[msolec]

For the one at 3:57 Couldn't you pick u=secxtanx (becomes integral u^2)