What Integration Technique Should I Use? (trig sub, u sub, DI method, partial fractions) calculus 2

So what integration technique should I use?

start: 0:00
integral of ln(x)/x^3, 0:45
integral of sec^4(x), 2:29
integral of (2x+3)/(x^2-5x+4), 3:50
integral of x^2*tan(x^3), 5:50
integral of 1/(1+x^2)^(5/2), 7:17
integral of e^sqrt(x), 8:50
integral of sin^2(x), 10:37
integral of 1/(sqrt(x+1)-sqrt(x)), 11:20
integral of e^x/sec(x), 13:15
integral of 1/(1+cos(x)), 15:09
integral of (x-4)/(x^4-1), 17:44
integral of x^2/sqrt(1-x^2), 19:24

#calculus #blackpenredpen #apcalculusbc

[blackpenredpen]

If you guys like this video, give it a like and share it with others!
Let me know if I should do a part 2 for this?

integral of ln(x)/x^3, 0:45
integral of sec^4(x), 2:29
integral of (2x+3)/(x^2-5x+4), 3:50
integral of x^2*tan(x^3), 5:50
integral of 1/(1+x^2)^(5/2), 7:17
integral of e^sqrt(x), 8:50
integral of sin^2(x), 10:37
integral of 1/(sqrt(x+1)-sqrt(x)), 11:20
integral of e^x/sec(x), 13:15
integral of 1/(1+cos(x)), 15:09
integral of (x-4)/(x^4-1), 17:44
integral of x^2/sqrt(1-x^2), 19:24

[ABruckner]

This is probably the most important Calc II video ever produced. It focuses exclusively on strategy, which is the most important element in all of calculus: Learning strategies (creativity), and recognizing when multiple strategies are valid, and why some might be better. Bravo, Steve! It's similar to your D/I "When to stop" video. Ever since I've stumbled on your channel, I've been re-learning calculus just for fun!

[neeraj]

What integration technique should I use?
Me: Wolfram Alpha

[josammarenye]

This guy is hilarious. He makes calculus look like primary mathematics. Can't thank him enough 👏👏

[spelunkerd]

This has to be one of your best videos, it really made me stop and think. The ability to stop the video, think the problem through, then resume is far better than classroom teaching of the past.

[MatthewChenIsAwesome]

"Take it to the u world" is now my favorite math phrase

[MisterTutor]

Integral Calculus can be summed as "What Kind of Magic Spell to Use?" :)

[holyshit]

For the fifth integral there are two u subs which work nicely
1. u=x+sqrt(1+x^2)
2. u=sqrt(1+x^2)/x
Integration by parts also works for this integral

[marrenroy]

This is great, my biggest struggle in calculus 2 has been that intuition you're supposed to have about what integration method to use. It does not come naturally to me, same reason the whole "guess and check" process of factoring quadratics was a nightmare way back in elementary school

[nlight]

bro just saved me from calculus. I've always wanted to create a youtube channel teaching cool stuffs instead of hiding them. You are my inspiration

[michaelsergi]

Honestly, as fantastic as my TA is, you are amazing. Both of y'all have done an amazing job at explaining and writing out problematic scenarios that give us lower level students the biggest issues. However you present these scenarios in all of your videos so well. Thank you very much. (note: calc2 student)

[letsseepaulallenscard.]

You are a machine, I’m very grateful for the daily uploads #YAY

[FridgeGames]

amazing video! really useful since I'm learning integrals right now

[sollertia_]

In essence, try thinking about using
trig sub: look out for single term square root denominators and 1+x^2 or 1-x^2
IBP: When you can easily differentiate one part and integrate one part
PFD: When the denominator is a higher power polynomial or when the denominator can be factorized (pretty much the same thing, but not quite?)
u sub: When the derivative of something can cancel out a troublesome part or when you're doing variations of a simple integration question but don't want to be careless (Feels like the most powerful and flexible tool in my elementary calculus toolbox, though, so probably has way more specific uses)

I'm not in uni yet or anything so I'm not sure if my insufficient contact with calculus problems has led to some mistake of some sort in the summary above so please let me know if there are better ways or corrections that I would want to know about, thanks~

[abhishekpatil]

In the first question, we can rather make a u substitution

Lnx= t and x = e^t
1÷x dx = dt

So the integral becomes

T÷e^2t dt
Then we can use integration by parts.

[THE-LIGHT..]

This is a fantastic work, I'm pursuing integration and calculus 2 courses so actually your channel becomes my favourite. Wonderful job

[Zephyr-tghu]

This was a really cool video. I especially love how you integrated e^sqrt(x)!! Very clever!

[abhirupbhattacharyya]

Best channel for learning U r the best😀😀😀😀

[charleswoodard]

This channel has been a vital supplement to my studies!

[teyhaleonard]

i have been looking for a video like this for ever ! I have not found one video breaking down the strategies you should use, which is the most important and confusing aspect of integration ! TYSM !!