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Partial Integration question watch

1. How do you partially integrate the following with respect to x?

(1/x)*ln(xe^y) dx

I used integration by parts to get:

ln(xe^y)lnx - ((lnxe^y)^2)/2) + c

But apparently the answer is just ((lnxe^y)^2)/2) + c?

how does the ln(xe^y)lnx cancel out?

thanks
2. Well one thought is that BTW, my answer is nothing like yours either, have I written the Q out incorrectly.? Here it is in tex
3. (Original post by zomgleh)
...
You don't need partial integration, the integrand is already in the form y'y. Anyway, you made a mistake when differentiating.
4. (Original post by zomgleh)
How do you partially integrate the following with respect to x?

(1/x)*ln(xe^y) dx

I used integration by parts to get:

ln(xe^y)lnx - ((lnxe^y)^2)/2) + c

But apparently the answer is just ((lnxe^y)^2)/2) + c?

how does the ln(xe^y)lnx cancel out?

thanks

using

and so
5. (Original post by Lord of the Flies)
You don't need partial integration, ...
Can you expand on that? The integral would be +f(y) rather than +C with p.i. I don't understand why you said "you don't need PI" surely that is merely irrelevant to the integration but the "answer" in the case of pi requires +f(y), so he does "need" it in the context of the question.
6. (Original post by nerak99)
Can you expand on that? The integral would be +f(y) rather than +C with p.i. I don't understand why you said "you don't need PI" surely that is merely irrelevant to the integration but the "answer" in the case of pi requires +f(y), so he does "need" it in the context of the question.
Not sure what what you're talking about, I merely pointed out that there is no need to partially integrate by noticing that:

7. I think I know whats going on here, the OP meant integrate "partially", i.e partial integration where x and y may both be functions of another variable, not by parts. Consequently, at the end, instead of adding C we have to add f(y).

I think you just meant that he doesn't have to use integration by parts. I think the problem is a bit artificial in the sens that it was constructed from a partial differentiation and then not simplified in order to create the problem.
8. (Original post by nerak99)
I think I know whats going on here, the OP meant integrate "partially", i.e partial integration where x and y may both be functions of another variable, not by parts. Consequently, at the end, instead of adding C we have to add f(y).
I have always seen the term partial integration as meaning integration by parts, and Google seems to agree - but perhaps it can also refer to what you mention. However, given that the OP said "the answer is ln(xe^y)^2/2 + C", and that they also used the term "by parts", I assume they meant integration by parts.
9. thanks for all your inputs, found the answer so thought of sharing it--

break it down into (1/x lnx + y/x) and integrate with respect to x.

and I meant partial integration, as in treat the y (and any other variable) as a constant, which is not to be confused with integrating by parts (which is something I used to integrate the function without simplifying it)

cheers

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Updated: March 9, 2013
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