Need help with an Integral Homework Question

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Homework Help Overview

The discussion revolves around evaluating an integral of the form ∫(dx/[(k1+k2)x-k2*y]), where the original poster expresses difficulty in arriving at the correct solution. The integral involves logarithmic functions and variable limits of integration.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to evaluate the integral but questions their approach due to discrepancies between their result and an expected answer. Some participants discuss the use of a substitution method to simplify the integral.

Discussion Status

Participants are exploring different interpretations of the integral and discussing the implications of variable limits. One participant has provided guidance on a substitution method, which seems to have clarified some aspects for the original poster.

Contextual Notes

There is a note regarding the unusual nature of having a variable as both a limit of integration and as the dummy variable in the integrand, prompting further examination of the setup.

juice34

Homework Statement


I am having trouble finding the right solution to this integral it is of the form int(1/x)dx=lnx+c but apparently I am doing it wrong because of the other factors in the denominator
integral(dx/[(k1+k2)x-k2*y]

Homework Equations





The Attempt at a Solution


i get (1/(k1+k2))(ln(x/xi))-(x-xi)/k2*y but apparently the answer is
(1/(k2+k2))ln[((k1+k2)x-k2*xi)/((k1+k2)xi-k2*xi)]
so what am i doing wrong
 
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please note that i evalued the integrals for both from xi to x also
 


Is this your integral?
\int_{x_i}^x \frac{dt}{(k_1 + k_2)t - k_2 y}

It's unusual to have a variable as a limit of integration that is also the dummy variable of the integrand, so I switched the dummy variable to t.

To do this integral, use u = (k_1 + k_2)t - k_2*y. Then du = (k_1 + k_2)dt. Can you finish this?
 


Thank you mark I understand now, you are a great help!
 

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