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

bro we learn that into calculus 1. Do we have problem :(

Well very good video its helping me in my high school calculus love from india

Bro , tienes play list de integrales , saludos

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Can you explain the exact nature of dx and dy? Since sometimes they algebraicaly participate and other times they don't participate at all. I'm a bit uncertain.

in example 1 why you not complete to take a derivative for 1/2x*2 to be 1/4x ?

Why we don't put the absolute value for answer of √(cos²(x)) and we write it cos(x) ?

Everyone talking about calc 2. We're doing this in calc 1😭. Thanks for the video!!! It helped a lot

I basically just steal your videos for tutoring material. I enjoy the clarity and the breadth of the content very very much!

Does Weierstrass also work for 10, with a different C value? It returned t, or tan(x/2) + c

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

Does anyone recognize the Doraemon music in the background at the start

I love you

thanks sir, you're such a wonderful teacher

I can't see the bottom exercises on the board because of the underlining



You are very clear in your problem solving... Keep up the good work

thanks, you help me!

I love the doraemon theme playing subtly in the background for the intro ^-^

I gave this video a try, as im stuck on an integral that i know can be calculated, but for some reason no matter what I throw at it, it keeps exploding into more garbage.

He drinks calculus 🥺

i cant describe how much i love you;

Aah all these are too easy

thank you so much! You've helped me alot in improving in calculus. I wish you get everything you've been praying for! Pray for me that I finish engineering school💛

But who can remember all of those things?? Every math book alwaya giving the basic formula, but difficult integration like those always case by case solution. That's why people keep flunked out with integration

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

for 10th one, we can also use
1+cosx = 2cos^2(x/2) which will give sec^2(x/2) which can be easily integrated.

I used another technique for the 10th
First, observe that cos(x) can be written using Euler's formulas. Now you can use u substitution twice. If u = e^ix, you're left with the inverse of a polynomial, 1/(u²+2u+1). The result of this integration method is (1-e^ix)i/(1+e^ix), which's in fact equal to sin(x)/(1+cos(x))

(The last step needs some clean up using Euler's formulas and a readjustment of the integration constant to get a function that goes from R to R)

Is this the " new math"? No wonder kids today are confused.

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

You made it look easy.

I did the second integral like this: sec^4(x)=sec^2(x)sec^2(x), integrating by part [the primitive of sec^2(x) is tan(x)] we have tan(x)sec^2(x)-2Stan(x)sin(x)/cos^3(x)dx (S is the integral sign) the inside of the integral is just tan^2(x)sec^2(x) so is a function f^n(x) times his derivative, where n is 2, so the resoult is tan^3(x)/3. putting all together we should have tan(x)sec^2(x)-2/3tan^3(x)+C. Is it right? And if it is wrong, can someone help me to figure out when i was wrong?

I did the second integral like this: sec^4(x)=sec^2(x)sec^2(x), integrating by part [the primitive of sec^2(x) is tan(x)] we have tan(x)sec^2(x)-2Stan(x)sin(x)/cos^3(x)dx (S is the integral sign) the inside of the integral is just tan^2(x)sec^2(x) so is a function f^n(x) times his derivative, where n is 2, so the resoult is tan^3(x)/3. putting all together we should have tan(x)sec^2(x)-2/3tan^3(x)+C. Is it right? And if it is wrong, can someone help me to figure out when i was wrong?

Thank you. This is the Best Video
I don't think I will ever fail to intergrate these kinds of🎉... Don't you have the one that includes the drawing of the right angled triangle

I still have nightmares about calculus in college. I never worked so hard to get a C. statistics was fun. really enjoyed that class. I am 59 and that was 40 years ago-some wounds never heal ha ha

dy/dx = lny - lnx

The way he sighs at every difficult question is so relatable. But the way he answers them so easily is not relatable at all 😂😂

Nice Explanation 🤓🤓

Ur a hero ❤thank u so much

For the 10th one using 1+cox = 2cos²(x/2) is much better

Let me just integrate by expanding the function to the complex plane and circle a keyhole curve around it 😅

Thank you !

Speak English clearly, sounds Chinese to me.

iam student inrwanda thanks help us mathematians

For the 10th one you can say that 1/1+cos(x)=1/2(1/cos^2(x/2))=1/2(sec^2(x/2)) integrating it’s just tan(x/2)

For the third one you can also let 2x+3=(2x-5)+8 then the second term is 8/(x^2-5+4) than you can write the denominator as it’s canonical form than you get some argth, this way is a bit harder but it’s an alternative I guess

e to the sqr root of x was the one I couldnt solve before the video thank you sir

My favorit teacher 😍😍