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anonymous
 5 years ago
Evaluate
anitiderivitive
5x^4 e^x^5 dx
I know I need to get the u and du, but what about this problem tells me to do that?
anonymous
 5 years ago
Evaluate anitiderivitive 5x^4 e^x^5 dx I know I need to get the u and du, but what about this problem tells me to do that?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the fact that the derivative of x^5 is present

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This one is a bit less obvious, but what part of this equation seems like a good candidate for a u sub?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not quite. But that does stand out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm looking at the \(e^{x^5}\) as being particularly ugly, and I'd like to have it be something nice like \(e^u\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You'll find that in the beginning, you are mostly just guessing at things to pick for u and seeing if they work out nicely. As you get more practice you'll be able to spot things better.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So you can certainly try working with the x^4 as u, but then you'll have \(e^{ux}\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And you'll have \(5u/x^3\) in front because your du will be \(4x^3 dx\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So that's a lot of mixed x's and u's.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Which often (especially in the beginning) means you're on the wrong track.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0When you are first learning u substitution picking a good u, should simplify the problem a lot. What did you pick for u?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok good. Yes. So what is dx in terms of du ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0du = \(5x^4 dx \implies dx = ?\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not sure I want to think I take derivative of 5x^4 ??? not sure

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, just divide. \[du = 5x^4 dx \implies dx = \frac{1}{5x^4} du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So now we have something we can plug in for dx and it'll cancel nicely with the product of 5x^4 out front.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so will I put e^u * 1/5x^4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Don't forget the 5x^4 you have in front of the e^u from the initial equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or reverse it 1/5x^4 first

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Neither.. Let \(u = x^5 \implies du = 5x^4 dx \implies dx = \frac{1}{5x^4}du\) \[\int 5x^4e^{x^5}dx = \int(5x^4e^u )\frac{1}{5x^4}du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you follow that and understand where each piece came from?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't really understand why 5x^4 stayed in front

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Where should it have gone? It's part of the equation, I can't make it evaporate ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0All I did was substitute u for x^5 and replaced dx with my expression with du.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But I can't do anything to the 5x^4 yet, because that's not x^5 = u.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Does that make sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But when we do that, we get something nice for our new version that should be easier to take the antiderivative of.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0?? (5x^4 * 1/u *e^u) * 1/5x^4 du

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0never mind th 1/u should be just 1/1 shouldn't it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Umm.. close \[\int (5x^4e^u)\frac{1}{5x^4}du = \int e^u\frac{5x^4}{5x^4}du = \int e^u du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can see that because it is all multipilcation no + or 

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so now will I replace u with x^5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0After you integrate then you replace it back.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0err take the antiderivative.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, later on they're going to tell you that antiderivatives are called integrals. ;p

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so will the answer be e^x^5 + c

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good!!!!! Thanks gotta go now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Though you should slap some parens in there for readability.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you type it that is. I'm sure it's written right on your paper.
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