Another u-subsitution example

[DyvekeDraws]

could you please start using a vector-based drawing software? I'm assuming you're using a tablet, if not - your mouse drawing is astonishingly good. This drawing software makes the videos look really unprofessional - and even though the content is superb, I did just try to find another video the first time around - so did my friends I showed this too. So just for visuals, maybe a vector-based one? Or at least a little higher resolution?

[DyvekeDraws]

@DyvekeDraws I'm sorry, I didn't realise the video was so old. Disregard everything but the praise!

[nelson1tom]

please do some harder U-sub problems.

[tommie997]

If someone could answer me I'd be very appreciative, why does -du/u^2 go to -1/u^2 if -du represents sinx ?

[nelson1tom]

@tommie997 same thing as if you were writing: a/b=a*(1/b)

[tommie997]

@nelson1tom Oh yeah... I only find calculus troubling in some areas because I did not have that rigorous algebraic backround but now I comprehend. Thank you

[NOMVrewq]

I turned sinx/(cosx)^2 into sinx.(secx)^2 and used the integration by parts. It doesn't give me the same answer. Can someone help me?

[thebigdille]

Based on the properties of integrals, you can take the negative out of the -sinx, which came from the derivative of cosx and put it outside of the integral. so you get... -s(1/u^2)du

[Eagles0818]

Thank you so much for these videos! You make calculus 1000 times easier to understand than the textbook!

[Afrish9ja]

isnt it 1/cosx^2 + C at the end?

[Micali711]

@Afrish9ja no because you have u=cos(x)

[1073601]

a shortcut is turning sinx/(cosx)^2 into secxtanx

the integral of that is just secx

[Has9H2O]

can you please help me solve these two u-substitution equations? it goes like this:∫ [(1+sin x)/cos x] dx where u = sin x and ∫ (sin x)^3 dx where u = cos x. I'm having trouble trying to solve trigonometric functions by substitution...any tips would help a lot...maybe some more examples would help me sal! :)

[lunch789]

Thanks Sal. Forgot how to use u-substitution. Now to try some fluid force problems...

[woo216]

and you can simplify 1/cos(x) into sec(x) if you want thanks sal

[dickweed1000]

i cant show my love for u in words

[theunlitshadow]

@dickweed1000 Use numbers hahaha :)



[enjoyablesounds]

cos^2 x is ridiculous notation. use (cos x)^2

Sal your videos are great!

[adrienspawn]

lol

"That's YOU. Cosine of X becomes YOU"

[angel209056]

why bother using u-substitution. it can be simplified to tanxsecx, whose antiderivative is just secx + C.

[noneexistingman]

isn't it suppose to be (secx)^2+c

[dazza2708]

This video is meant for those who dont know secx cosecx cotx ...but yes you are right.

@noneexistingman

the answer is secx (+c) not sec^2x (+c).

[geek3333]

How do you solve a think like this:

1/( ( ( x ^ 2 )+5 ) ^ 2 )

P.S:I know the basis of rational functions derivatives.

Thanks in advance.

[vyaz1]

Thanx soo much... if only my lecturer could speak as properly as u do- i'd have learnt this section as soon as it was taught

[kylep2212]

Learned

[gyuziburcsany]

Great videos. I mainly fail at maths, but i can do a lot of calculus because of ur vids... and holy crap im a high school student

[BlackAdder6]

Last minute refresher for the AP calc test.

and I am wishing I had found you at the start of this school year cause, well, you blow my teacher way out of the water

[chriskill08]

ignore that last question....what is the DERIVATIVE of (minus) -ln(cosx)^2? is it sinx/(cosx)^2

[ultratribalist]

it is 2tanx lol,how is that possible.

i will use the symbol * for multiplication.

Y=-ln(cosx)2

dy/dx=-1/cosx^2 * 2cosx * -sinx then the two minus cancel each and also cosx cancells one cosx and we left with

dy/dx=2sinx/cosx which is the same as 2tanx.cheersssssssssssssssss

[ultratribalist]

sorry (cosx)^2 cancells one cosx in the numerator.

[cgvedant]

@chriskill08 2*tanx

[chriskill08]

what is the anti derivative for (minus) -ln(cosx)?

[mak47i]

you can make it easier  2

sinx/cosx= sinx/cosx*1/cos=tan*sec

S(secx*tanx)dx=secx+C

[iluvjiyongx3]

omg! u can scroll down now!!

and thanks for another helpful vid!

[VladimirVichfret]

great videos :D

[acidwillburnyou]

E.engineering student from UWaterloo here. Thanks for your videos. They are very clear and a valued supplement to school material. Keep it up!

[lydiargh]

thank you so much!!

[aznmonkey2010]

I just learned this in school . i'm so proud of myself for knowing this. thanks for all the vids. they're helpful

[Ritzoid]

Awesome man! I had to subscribe cuz your vids are top

[Painfoot]

I would have never thought to use u-substitution to solve that! It's more intuition on why trig integrals and derivatives are so. Although u-substitution is still a bit fuzzy for me...