Calculus

[AbysmalGuilt]

Someone want to help meh out? I have two probs, I know some of you are math wizzes from reading the last math thread.

Anyways, problem:

Evaluate the integral. Solve by the simplest method--not all require integration by parts. (I don't know how to make the integral sign so you'll have to assume it's there.)

(x^4)(lnx)dx

and

1/x(lnx)^3 dx


First problem, toughest thing is, since I'm trying to make lnx my dv, I dunno how to integrate lnx. I looked this up and it said make lnx my u since it's easier to find the derivative for it (which it is) however, it never comes to a 0...

Suggestions please. You don't have to answer it for me, but any hints will work. Thanks much.

[Jerov]

Someone want to help meh out? I have two probs, I know some of you are math wizzes from reading the last math thread.

Anyways, problem:

Evaluate the integral. Solve by the simplest method--not all require integration by parts. (I don't know how to make the integral sign so you'll have to assume it's there.)

(x^4)(lnx)dx

and

1/x(lnx)^3 dx


First problem, toughest thing is, since I'm trying to make lnx my dv, I dunno how to integrate lnx. I looked this up and it said make lnx my u since it's easier to find the derivative for it (which it is) however, it never comes to a 0...

Suggestions please. You don't have to answer it for me, but any hints will work. Thanks much.

Ok, so the second one is really [(1/x)(ln|x|)^3]dx, and you want to integrate. Well, first hand I'll give ya the derivative of ln|x|, which is 1/x. And the derivate you're given has 1/x in it, so it has to come from somewhere. Hope this gives you a big enough hint.

Edit: whoops! sorry if I'm confusin ya too much bud, been a long time. Here's the integration by parts rule:

Given an integral, we can treat it as the integral of f(x)g'(x)dx, which then we can then do f(x)g(x) - the integral of f'(x)g(x). Now, personally, here's what I'd do. You see that ln|x|? You can now do something with it and make this a whole lot nicer. Once again, sorry for the gibberish earlier, I needed to get my facts straight

[AbysmalGuilt]

Ok, so the second one is really [(1/x)(ln|x|)^3]dx, and you want to integrate. Well, first hand I'll give ya the derivative of ln|x|, which is 1/x. And the derivate you're given has 1/x in it, so it has to come from somewhere. Hope this gives you a big enough hint.

For the first one, now that's a pain in the ass. Mmm....there's a section on integration by parts. I think how it goes is say you have an integral you can treat as dudv. What you want to do is udv - the integral of vdu. So what I would do to start is pick your u to be the easiest one to use, while leave in the integral that's giving you a pain which you can integrate alright by itself.

If you want a hint on a proper u, just ask

Edit: Oh, I know how to do this problem now. Alright, in order to integrate ln|x| properly, given vdu, with v being ln|x| and du being x^4, here's a big hint. What's the derivative of (ln|x|)^2. Then take a look at du. Something is counting down as you integrate by parts over and over again

That's my problem, I'm not able to integrate lnx for dv, I know to pick easiest as u.

[Jerov]

Nonono, don't integrate ln|x|, that's not the point behind integration by parts. Treat ln|x| as your v, so the original integral right now is vdu. So now what this will turn into is vu - the integral udv. Try that bud. If it works, then the new integral you create in the difference should be MUCH easier to integrate

[Mil0]

**** math they are lying to you, you will never really use it.

[Chaotix]

what. the. ****.

[Mil0]

Just when the teacher comes to check your homework be like, See i woulda done it but then it hit me I didnt want to do it and id hate to punish my self like that, she'll just call your house and you can handle that with the simple SHUT THE FUUront door