How do I integrate u^-1 with new limits after substitution?

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Homework Help Overview

The discussion revolves around the integration of the function u^(-1) after performing a substitution in a calculus problem. The original poster expresses difficulty in integrating this function with the new limits of 1 and 2.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to integrate u^(-1) but feels stuck due to their current understanding. They question whether a linear expression is necessary for applying the natural logarithm in integration. Other participants engage by clarifying the nature of linear expressions and suggesting that the natural logarithm can be applied in this context.

Discussion Status

Participants are exploring the integration of u^(-1) and discussing the application of the natural logarithm. Some guidance has been offered regarding the use of logarithmic integration, but there is no explicit consensus on the final outcome.

Contextual Notes

The original poster mentions a lack of familiarity with the Latex system, which may affect the clarity of their expressions. There is also an implication of imposed homework rules regarding the problem setup.

markyp23
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Homework Statement



problem.jpg



Homework Equations



None. Well, dx=du/cosx

The Attempt at a Solution



I've substituted it in, got new values for the limits but I have u^-1 on the bottom and so can't integrate it from my current knowledge. Basically I'm stuck with:

Integration of u^(-1) du with limits of 1 and 2.

Any help appreciated. Apologies for not being able to work the Latex system.
 
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Seriously, you haven't encountered the derivative of the natural logarithm yet?
 
I have but I thought it had to be a linear expression to use the natural log. It did cross my mind though - this is what to do, then?
 
What do you mean by a "linear expression"??
 
Something of the form (ax+b).

Decided to assume that (u) is in that form and so worked it through. Is ln(2) the final answer?
 
Ask yourself:
May we write u=1*u+0?

Sure, the answer is ln2
 
Thanks for your help! :)
 

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