U-Substitution Example 2 (KristaKingMath)

How to use u-substitution to evaluate an integral.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[kristakingmath]

You're welcome! Glad I can make them . :)

[kristakingmath]

yes! you can take the derivative of your final answer to see if you get back to the original problem. The "+C" will disappear because it is a constant, and the derivative of any constant is 0. i hope that helps!! :D

[kristakingmath]

It'll be all because of you! You're putting in the work. :) But I'm glad I can help! Good luck tomorrow!

[kristakingmath]

you'll always have to decide what u is going to be, because it's not usually given to you. if you have a value inside parentheses, it's usually a good bet. and if you try it and it doesn't work out, pick something else for u and see if that works! :)

[kristakingmath]

@FredabkaFree Wow! Quite an endeavor to get back into DiffEQ, good for you!! Thank you so much for your support, and best of luck to you with grad school!! :)

[kristakingmath]

@RachowlKayeEM You're the one still doing the work, but I'm glad you find my videos helpful :)

[jomosoft]

Thank you so much for your videos ! They are very helpful and enjoyable. These are a great addition to my Open University study.

[delavega]

I finally understand how to use substitution. Thank you so much, you really are a great teacher

[kristakingmath]

You're sweet. I'm just glad you think the videos are helping!! :D

[streblo]

Are you such an amazing teacher! Everything is so clear and concise! Keep on teaching! Totally subscribing!

[kristakingmath]

you're correct that it would be -5 if you were taking the derivative. but in this problem we're taking the integral, aka the antiderivative, which is the exact opposite process of taking the derivative, and therefore the exponent becomes -7 instead. hope that helps! :)

[clamclam]

I love you so much!! I was gonna cry 'cus I was scared of the this part of my math final and then I found you. I now understand what happens to the du and dx. You are by far the best integral explainer. Ever. <3

[kristakingmath]

@delavega92 Thank you, and I'm so glad it's finally making sense! :)

[SKeeZy]

I can't thank you enough for your help. You are an answer to prayers! Ha, so is my wife but she doesn't like math. Thanks for all your help!

[georgebaidoojr]

Thank you. It starting to make some sense, when dealing with integrals. Huge lifesaver.

[kristakingmath]

No, you need to use u-substitution, or integration by parts, most likely. The method you use depends on exactly what your integral is. If u-sub doesn't work, try integration by parts. :)

[kristakingmath]

Yay! I'm so glad I'm able to help along the way. :)

[jayceinfinitealgharhythmns]

I actually solved this by watching the previous example! Thanks for the great work, it's much appreciated!

[joyeshakash]

You are awesome! And your examples really helped! ALOT! :)

[mikeram]

Thank you thank you thank you! I have a test tomorrow and I had no idea how to figure this stuff out! Now it all makes sense. Your the best!