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? Here's the file: docs.wixstatic.com/ugd/287ba5_f1afe86da0454ef08c92eae9b9e9c18c.pdf Here's the playlist to the solutions to everybody kzfaq.info/sun/PLj7p5OoL6vGwS5ilte_7fjRB2rQ_yE_Hj 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

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!

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

What integration technique should I use? Me: Wolfram Alpha

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

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

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.

his energy is so pure 🥺

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

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)

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

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

For those that want more practice, I have several videos where I solve complicated integrals step-by-step, using all the methods explained here. :) It might help some of you out there!

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

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

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 !!

Hi, I love your videos. Ii used to doubt my ability to do integrals but you make it so easy. Thank you for sharing your knowledge and techniques. You are an amazing person to do this vlogs.

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

you are literally like my cal 2 professor! and i love it! I watch these video to help in-force what i learned in class.

This is one of the best KZfaq video I've seen so far ! Thanks a lot !

Thank you for your kindness in making these videos. I love how happy you are and smiling, it helps me stay positive during math. Thank you!!

Well that's going to actually be some of the best revision I've got for my calculus exam in 4 hours :)

Hey man !! That's just awesome kinda stuff, can't really tell you how much your videos help me in my integration sums 👍👍👏 keep up with the great work.

This was perfect. I have my midterm coming up and this was the perfect way to study as you give subtle hints without revealing the whole answer. Thankyou very much

just took my calc 2 midterm and definitely did well thanks to your videos. Thanks!!!

I really appreciate and follow up ur tutor regularly. Wow i've got a lot of knowledge in easy way and surprised ur broaden mathematical wisdom. Mathematical difficulties of both derivatives & Integration become easy with ur lovely way of teaching methodology. Many thanks indeed. NA from Ethiopia

I will definitely be using your wonderful examples with my students of calc 2 class (which means we are allowed to use L'Hospital rule as well as Taylor series for the limit of sinc(x) :P

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

Wow. This video simplified so much for me. I wish I tuned into the channel ages ago!

Great calc 2 video. Its a good refresher. Im going to write down these problems to have a set of problems to practice.

Ever since i found this channel, i started learning calculus and complex numbers with curiosity and for fun 😃

This channel has been a vital supplement to my studies!

My master, I don't know how I should express my feelings right now. Thank you very much for this video 🙏.

shouldve had this on my recommendation two years ago. a life saving video

This is awesome I literally have a test on this tomorrow thank you so much!!

You are doing a great service for the world. Much respect sir

Excellent video, as always. Part 2 PLEASE

Cleared a lot of concepts in just few minutes ,👍🏻 appreciated bro

Why are you using a magic 8 ball as a microphone?

Great video. I love how even spiderman is one of your patrons.

ive got a calc midterm in two hours, this has helped immensely, thank you so much

Happy Easter! Much health, happiness, peace of mind, peace. Thank you!

Thanks a lot dear brother. Want to meet you in person and say " Thank you "

This video and the DI method video makes me feel like I’m learning something illegal! Haha I’m serious, you have no idea how much you’re helping me!

I'm glad I've had a great calculus teacher . I can understand all this

Please this video should be given an award as the best integration simplified video ever 👌👌

please put part 2.this video is really helpful

Man those videos are some gold

Thank you very much for this video it was very helpful I have had trouble with question number 6 but after seeing the solution you have explained I satisfied with it 🙏

This man is saving my Calc Grade.

Beautiful!!! Waiting for part 2

Uploads like this

I’m so glad BPRP has such a big following, you always make me smile even when I see a very hard problem that I can’t fathom in your vids! I really want to become smart like this guy!

thanks for video, very nice nad helpful, now I understand the meaning of trig subsitution a little bit more.

You are amazing man A great teacher You make integrals seem so easy 🤩

What you offer is a blessing for others

Great Video! Solving integrals is allways fun!

Thank you so much i am in highschool right now and this is one of my major problems i cant seem to think what to do next You helped me soo much with your videos I sincerely thank u for ur hardwork!!!! :)

Thanks a lot for this video. These videos are saving my life!

Thank you your videos are si helpful I have a midterm exam I this will definitely help me

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

Can you show an integration where you have to use all these techniques together? For example: first you have to integrate by parts, then make u-sub, then trig-sub? It would be very nice.

Thank you for another fantastic video!!!

Excellent work!

love these videos, super useful and funny too!

YAY!!! I downloaded your worksheet just 1 hour ago i got em' all. And for the first integral we could also let u=ln(x) that can work too. Anyways KEEP UP THE GOOD WORK because this channel ROCKS....!!!!

Awesome video! So helpful! I love your personality! God bless.

For #12 you could let u = arcsin(x) for the fun of it.

You're indeed Mr Calculus Finisher. You're the best Sir

problem #3 and trig sub is never talked about enough in calculus. Amazing video watched it twice!

I really learned a lot in your videos, especially the 100 integrals you solve. Aside from the fact that I like your speaking tone and explanation and lastly your eyes. So cute.

omg thank you so muchhh!! This was incredibly useful. God bless you :D

Thank you teacher

In the 10th question, you may write the denominator as 2cos^2(x/2) using the half angle identity and then write it as sec^2(x/2) and proceed from there.

He’s literally so much better than any other teacher out there.

man, u r very good at this!

his smile is way much appealing and makes session kinda more interactive :)

Love your effort sir... Love from India. Thanks

IN the beginning of the video he said that there will be some calculus 2 in this so I said I will concentrate on things I learn in calc 1 since I didn’t take calc 2. To my surprise I took every thing he explained in the calc 1 course in my uni. Now I really believe my uni is super super hard, I wonder what they’ll teach me in calc 2

hi dude, I'm so grateful seeing about you 'cause you really have been so useful for me, you don't imagine how, and this time I need you again, I wanna ask you ¿when should I solve an integral multiplying for the conjugate ??

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~

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.

thanks sir, you're such a wonderful teacher

Thank you so much i had problem on integrating techniques

This is the greatest thing to ever have been produced.

please make a part 2 for it I really need it to get a proper feel of the topic

Excellent lesson on integration!

One of your best. Thanks

Nice secession ... brother .... good effort 👍👍👍

nice bro.. im actually studying calculus in chinese.....this really cleared up a few things

Amazing teaching skill and strategies

for the 10. integral you could use substitution u=tan(x/2), it's a beautiful substitution that works every time in integrals where you have sin,cos,constants and their addition

You're one of the best KZfaq has ever had

Actually in the first one, 'u' substitution is going to work. We substitute 1/x as u and we integrate to get (dx×-1/x²)=du. Then we take the natural log on both sides of the 1/x=u and get -ln(x)=ln(u). Then we can substitute all the values to get u×ln(u)du as the integrand. Cheers

You are awesome. This video is awesome. Awesome content

i cant describe how much i love you;

Appreciate you 💓 , you deserve it..

Very helpful. Thanks a lot.

Very good video !

Nice work sir