glad i was able to help : )

Patrick, you are a wonderful human being. Thank you so much for your contributions to the mathematically challenged!

You are a gift to all of us who need your wise teachings amongst a barren idiotic world.

A hero of students who goes to youtube instead of listening to their teachers. :D I'll give you a medal for that Patrick!

I was in tears until I started watching your videos. thank you

hope this doesn't come off as weird, but you are one of the most intelligent individuals in the world because of your ability to teach difficult concepts to others in an effortless manner. you were born to do this.

YOU MAKE FEEL LIKE A MATH GENIUS! which I'm not but that tells a lot about YOU rather than me! You're the best Patrick. wouldn't have gone through first year engineering maths without you.

thank you very much , you've helped me a lot , i'm from Saudi Arabia and my teacher doesn't revise with us before exams , but from now on , i think i don't need him any more .

these videos have seriously been a life saver, thank you

14y ago vid and nowadays teachers not doing this topic. You are only saviour here

Safe to say, best, easiest to understand maths tutes online. Gone from barely passing to aceing maths. Cheers mate.

THANKS SO MUCH! THIS LITERALLY SAVED MY LIFE. I have a Exam tomorrow and had no idea what to do after using the double angle formula once. Thx again!!!!

Thanks a lot Patrick, I really appreciate your help on everything man. The way you explain this stuff is so clear. Other professors make this stuff that's supposed to really be as easy as you show it, hard as hell!! Thanks again bro and I will keep watching your great videos

Extremely beneficial. I have been terrified all week about my upcoming test because I have no idea what my teacher is talking about 95% of the time. These videos have definitely clarified what my book and teacher cannot. Thanks!

yea, i agree the audio in a few sucks. i think i have that fixed now, and it should not be a problem in any more of my future videos. i am learning the technical side of production making these videos : )

Patrick you got me through calc 1 and im still relying on you for calc two so please dont stop making these videos they are so damn helpfull.

I have a calc 2 test next week and this is so helpful, thank you!! I couldnt even math before this 😭😭

you have literally saved my academic career. my calc professor is great, but teaches at ungodly speeds during his lectures. you have slowed everything down and have pretty much answered all of my questions about pretty much everything up to this point. just wanted to say thanks haha

Thanks soo much for this video, I was struggling on a problem like this and found that that it has to be really a tedious problem when integrating even sin and cosine functions!! THANKS SO MUCH!!

Thank you man. I needed this so badly.

This is incredible. Thanks so much and God bless!

u re really helpful u ve made it easier for me.. thank u so much.

thank you! this is really helpful.

Professor Patrick, your teaching is godlike!

I love you so much, thanks a lot you're a life saver!

i really thankful that you have a video like this it really helps!=)

Only 40,000 views? that shows how very few people take math seriously. I am thankful for patrickJMT because he makes this blurry vision of Calculus a lot clearer.

Patrick you are the best!!!

Thanks a lot this really helps.

Thank you, you make it simple.

You are the reason I am getting through engineering haha

really good at explaining, thank you

Patrick, the math maker. I am glad I met you. Oh, yes, thanks a million.

@Sarah Hudak The formula is for cos^2x but the term in the red bracket is cos^2(2x). The coefficients get multiplied. 2*2, hence the 4x.

Thanks u so much 4 this, Patrick! Yesterday in a test i couldnt do it, now i know lol :)

It was so long way to find it,you can find it simply without using u substitution,but thank you,your videos so helpful))

A big thanks for the time to supply these vids. These and your site have been extremely helpful. Only -ve comment is the distortion when you speak to loud into your mic.

Great video, your trig integral videos have been a big help! For this particular problem though i found it much less tedious to just rewrite (Sinx)^2(Cosx)^2 as (SinxCosx)^2 and then use the identity: SinxCosx = 1/2Sin2x And because we have (SinxCosx)^2 that would equal 1/4(Sin2x)^2. Then use u-substitution for 2x and just integrate 1/8(Sinu)^2. But thats just what i wouldve done. I guess i try to avoid the other identity that you used because i find it can make things messy sometimes lol thanks again!

I have a calc 2 exam later today, this video just saved me!!!!

It's not always that the professor is bad, it's that Patrick is just so good.

Very helpful. Thank u

Patrick, all I can say is THANK YOU SOOOO MUCH!!!!!! I'm not joking, you are a great teacher. Calculus is hard, and trig. sub. is even harder, but you make it seem simple and straightforward. Thanks again :) ps. would you be make more videos? I think everyone would love that. :)

Great info!

no one is as awesome as you are on youtube

I'm doing practice for an upcoming exam so I stopped the video just as you identified the problem here and worked it through. I got the same answer as you, but in seemingly far fewer steps.. I basically put parentheses around the entire sinxcosx expression and squared the entire thing (sinxcosx)^2 and from there used the double angle identity of sin2x/2 in its place. Squaring that gave me sin^2(2x)/4, pulled the 1/4 out and converted the sin^2(2x) to 1/2(1-cos(4x). Multiplied the 1/2 through and then took the integral. No need to foil anything. Guess there's always more than one or two ways to skin these kinds of cats. :)

Thank u so much prof

You saved my life!!

Keep it up! You're awsome!

this is very great..thenkyuh so much..

maaan, thank you so much!!

u deserve money. lots. i pay this school so much but you teach it better.

glad i could help. and : key lime or buttermilk would be great.

After watching your videos I have one major and serious regret---I regret not knowing about your videos my freshman year of college. If I would have, I would've done a lot better. You're a perfect teacher. Thankfully I have your videos at my disposal entering my sophomore year. God Bless

Thank you so much

Thanks a lot for giving a better explanation and i hope this topic i can report well to my classmate ^_^

My integration techniques leveled up watching this video!!

omg are ya a guru,cos ya need to get some creds for dis awesome stuff ya doo,thanks a span man

Thanks for help sir how can we integrate cos^4(x)*sin^6(x)?

when i thought he was done...he kept going!! x_x

U-substitution when integrating cos(4x) isant needed it would just be sin(4x)/4 because of the chain rule.

thanks chap

How do you integrate ones with two odd numbers as their Power something like this integral (sinx*cos^(3)x)dx

thank you for sharing your knowledge in calculus

umaiththa,you are the best

yes, there is some identity you can use to speed this up. i know this works though, so i have never bothered to think about it anymore : ) however, feel free to play with is and get back with me! : ) as erdos would tell you: this is a $1 question

best tutor eveerr, you actually take the time unlike professors

youtube is made for patrickJMT!! UBER THANKS DUDE! :))

all of it. it was all relative to what i understood up to that point. eventually it gets beyond what i can understand

THANKS!!!!! You explain very well and your website is way better then khanacademy :D

ok, i added the tags :)

How do you determine which factor you will expand? In the previous video you expanded expanded one factor, in the video above you expand both.

Great video man! you be left handed is a real bummer though. It's hard to take notes after you.

Thank you.

Thank you

yes. So long as it is something that you can factor out of the entire piece that you are integrating: for example, you can take the integral of int (5x^2.+5x)dx = 5*int(x^2+x)dx It's kind of like taking out a common factor (so long as there is no variable in which you factor out, because you need to integrate the variable). Sometimes this helps you, and in some cases it doesn't.

can do u more integral with a lot of trigo. identity. I'm still struggling of integration

deeply appreiated

why do you get - 1/2 cos(4x) when you distribute 1/2 into cos(4x)? wouldn't it be positive 1/2 cos(4x)?

*.* you just explained in 2 minutes what i have not been able to understand for a day and a half, I hope KZfaq has made you a partner and pays you

you helped me out better than my prof did

I LOVE YOU !!!

how are there only 17000 views, it's the greatest!

@marymc14 It's suppose to be a formula. A half- identity formula that you have to use when integrating even trigonometric functions

at 5:08 I was also like "oh dear god what are you doing putting du!" Just kidding lol If I could no longer go to class and just learn from you it would be so worth it

thank you so much,now it will be easy for me to finish my homework... at 5:28 why at the second step written 1/2 dx...then later at the next step it became 1/2x.... but seriously this video help me a lot.thank u =)

Thanks man..........

Is there a way to know when to use the double angle formulas rather than replacing sin^2(x) with 1-cos^2(x) and cos^2(x) with 1-sin^2(x)?? thanks

My Russian professor went over this today. He doesnt smile. And he never understands our questions. You are so much easier to understand and follow. He spent about 25 minutes on an even powers trig integral problem, where you did it in

I love u man now I understand everything! Keep up the work

I got the same answer without using the u-substitution. Is the u-substitution necessary in this case?

hey Patrick i tried removing the 1/2 as a constant in both terms be for i went on to further integrating it but 1/8 | 1 - cos(4x) then 1/8 | 1 - |cox(4x) let 4x + u so du = 4.dx then I dont get why you wanted dx to be the subject of the formula when now where deling with du, anyway after that i got 1/8 | 1 - |cos(u).du < we are still using du.... finally I got 1/8x - sin(u) = 1/8x - sin(4x)... so i don't know where i messed up.

can you do one that has something like the integral between pi/4 to x^2 of sin^2 (tan t) dt? Im a little confused about it.

Great example

thanx!

Wow, that answer just makes you all the more awesome :)

thank you for the video patrick.. but i gotta ask.. in different trigonometric techniques of intergration. aren't we suppose to use by parts instead of U substitution?

Bro!!!! You're my hero!!!!!!

Ok this is my problem with these kinds of questions, when do you know when to stop trying to find something to substitute (or use u-subs, simplification) and consider it as the final answer? like 5:32, i would consider that as done already? what is the main criteria to consider it as the final answer?

Patrick What do you do if it is a definite integral?! At the end i just plug in for the postive powers of sinxcosx at the end i plug in pi/2 into the x's?

Is it necessary to do u-substitution again on (cos4x)/4?