Integration using U-Substitution

Visit : http://bit.ly/pTquLB for your 14 day free trial at Thinkwell! Videos, Quizzes, Tests and More!
Integration using U-Substitution of Indefinite Integrals. For more free math videos, visit http://PatrickJMT.com and click on your subject from the left! I have organized links to TONS AND TONS of math videos made by me!

Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor

Category:

Education

Tags:

• substitution
• U-substitution
• Integration
• Integral
• Calculus
• math
• austin
• tutor
• ACT
• SAT
• AP
• BC
• justmathtutoring.com
• usub
• u-sub
• educational

[WindBreaker77]

Anybody else had that awesome moment when you finally understood?

[patrickJMT]

@WindBreaker77 i have had many in my life :)

[NotAllanHuynh]

Night before a midterm. All feels hopeless. PatrickJMT. Never fails.

[patrickJMT]

@NotAllanHuynh good luck! :) 

[Minishglob]

i coundn't figure out what the dx in 'du=2xdx' means. does anyone know what the dx from 'du=2xdx' mean to the first problem (excercise) in the video?

[patrickJMT]

@Minishglob the infinitesimal

[fadedBl00d]

hey, for the last type of problem my teacher wants it simplified further, would factoring out (x+2)^(3/4) and then distributing the fraction and factoring out the fraction be incorrect? After I did that i got (4/21)((x+2)^3/4)(3x-8), is that correct?

[erectance]

@NotAllanHuynh same here

[kattunluver16]

I really appreciate what you do :)

[mushuhead88]

thank you so so so much. i understand this so much more now

[NoDoubtFilms]

Thanks for taking the time to do all these videos. Every time I don't understand something, you always seem to have a video about it.

[kennethkrist]

@kennethkrist The point is following:

You have: dx = du / (f(x))'

That means you can replace [dx] by [du / (f(x))']

Hopefully (this is the point of substitution) you can get rid of any x in your integral because in the above expression you get to divide by (f(x) derived)... Then you should be getting an integral with only u's instead of x and the more complicated the U you choose, the simpler your new integral should get IF you get rid of all the x's...

[kennethkrist]

@Minishglob When you substitute, you put u = something.

When you got u = something, you can derive the expression with respect to the variable (often x), here using f(x) instead of x^2 as a more general example:

u = f(x) => du/dx = (f(x))'

du = dx (f(x))' or dx = du / (f(x))'

When you got an integral with dx where you choose to substitute, you can use the above algebra and derivation to replace both the core ("Stuff on the inside") and the dx with terns respecting u instead of x.

[claire383]

Thanks this was super helpful! :)

[LSGBeats]

@NotAllanHuynh good luck! :)

[Dubbidubdub]

Sorry, but I'm very new at this and confused. For example one, why do you find d/x of x^2 + 4 if you are integrating, not differentiating. And why is is 2x d/x, not just 2x. Why do you need the d/x. If you told me to differentiate x^2, I'd just say 2x.