calculus help....

[MetalGrasshopper]

Re: calculus help....

wouldnt it be 1/p+1 times x to the p+1?

[TheSteveMan]

Re: calculus help....

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You have to do integration by parts.
You'll have to take the integral of one of those inner functions, and the derivative of the other.
Since ln(x) is easier to differentiate than to integrate and x^p is not that hard to do either way, I'd go with differentiating ln(x).

The answer will be [ln(x)*(1/p)*x^(p+1)] minus the integral of (1/p)*x^(p+1)*ln(x)

Then, that integral should be easy to evaluate by substitution of variables because you have ln(x) and its derivative, 1/x in the same function.
Let U = ln(x), then x^(p+1) is equal to (E^u)^(p+1)
If you need more help, let me know.

By the way, this is assuming p is a constant.
If you are in vector calculus and p is a variable, sorry but I can't help you yet [img]/images/graemlins/laugh.gif[/img]

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Yea I was supposed to do it with integration by parts, but I got a really fookin ugly answer...

ln(x)[x^(p+1))/(p+1)] - [x^(p+1)/(p+1)^2]

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I know what you mean-- there are so many ugly looking problems in calc that come out with these sweet answers, but sometimes an ugly looking answer is just part of math.

In my calc 3 course, when we wasted a couple weeks on fucking ass crappy arc-length and surfaces of revolution, it was kind of like that.
The arc length formula is:
Arc length of a function from A to B =
Integral from A to B of Sqrt[1 + (dy/dx)^2] dx
Now, unless dy/dx happens to work out to something with the square root of x, or you happen to have an x on the outside of the function (which happens with surfaces of revolution) you have to integrate something that looks like Sqrt[1+x^2] or something shitty like that. Sometimes 1+(dy/dx)^2 works out to be a nice polynomial that happens to be a perfect square and it's all nice, but that's only if you're lucky.

Once on the homework I got some answer to a word problem that involved ArcSinh of some different terms.. I got marked down most of my points for not giving a NUMERICAL answer (most teachers accept exact answers, which look nicer)

Unless you happen to know how to take ArcSinh in a calculator (I don't, we never covered it in class) how the hell was I supposed to do that?

Bah!

OK I'm done bitching about that...

[TheSteveMan]

Re: calculus help....

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wouldnt it be 1/p+1 times x to the p+1?

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Yeah you're right.
Damn I'm terrible with this crap if I'm trying to do it over a computer and not by hand!

[TheSteveMan]

Re: calculus help....

Hambucker it only looks kind of ugly because p is a constant which is undefined and you have to throw around lots of 1+p things and whatnot... you're def. right it looks nicer if you put an actual constant in there.

[YetAnotherOne]

Re: calculus help....

I suddenly remember why I gave up engineering and went to law school. [img]/images/graemlins/laugh.gif[/img]

[Deneb]

Re: calculus help....

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Get offa my lawn, you punks! [img]/images/graemlins/laugh.gif[/img]



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He's just mad it's not English homework.

[RacerX]

Re: calculus help....

[img]/images/graemlins/laugh.gif[/img] I know you need some help in that area, huh, Den Den?

[TheSteveMan]

Re: calculus help....

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I suddenly remember why I gave up engineering and went to law school. [img]/images/graemlins/laugh.gif[/img]

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Are you joking? Math is easy!
I wouldn't last a day in law school, however.... [img]/images/graemlins/laugh.gif[/img]

[YetAnotherOne]

Re: calculus help....

[ QUOTE ]
[ QUOTE ]
I suddenly remember why I gave up engineering and went to law school. [img]/images/graemlins/laugh.gif[/img]

[/ QUOTE ]

Are you joking? Math is easy!
I wouldn't last a day in law school, however.... [img]/images/graemlins/laugh.gif[/img]

[/ QUOTE ]

I got out, I just didn't get out in time. I wound up with a couple of engg. degrees and 30 hours towards my Ph.D. along with a few years of orbital analysis and telecom traffic projection. When I reached the point where nothing in my field looked like as much fun as what I'd been doing the past couple of years I figured it was time for a change. [img]/images/graemlins/laugh.gif[/img]

And you'd do fine in law school, by far the hardest part is getting in.

[monk]

Re: calculus help....

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Can someone help me find the integral of (x^p)ln(x)dx? thanks!

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You have two cases:

Case 1 (p = -1)

int[ln(x)/x] = (1/2)ln(x)^2

Case 2 (p != -1)

int[(x^p)ln(x)] = (x^(p+1))[ln(x)/(p + 1) - 1/[(p+1)^2]]

[Deneb]

Re: calculus help....

Usually, mine, is, great, but, I'm, in, a, bad.


ergh

Usually min'e pretty good, but I've been using a lot of commas lately. I've not even noticed it, until it was pointed out to me.

I've got to quit that.