Integration of an inverse function

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Homework Help Overview

The problem involves integrating the function \(\int\frac{4}{x(x+3)}\), which falls under the subject area of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use substitution but finds it complicates the problem further. They express a need for guidance. Another participant suggests using partial fractions to decompose the integrand, which may simplify the integration process.

Discussion Status

Participants are exploring different methods for solving the integral, with one suggesting partial fractions as a potential approach. The original poster is seeking clarification and support, indicating an ongoing dialogue about the best method to apply.

Contextual Notes

There is mention of the original poster's lack of recent math experience, which may influence their approach to the problem. Additionally, a note on the distinction between "reciprocal" and "inverse" functions suggests a potential area of confusion that could affect understanding.

iceman_ch
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Homework Statement



[tex]\int\frac{4}{x(x+3)}[/tex]

Homework Equations





The Attempt at a Solution



I can get to s certain point and I know I need to do substitution but, everytime I try a substitution it just creates a more difficult problem.

[tex]4\int(x^{-1}(x+3)^{-1})[/tex]

I've tried substitution x^-1 for U and using (x+3)^-1 for dv but, none of it works. If someone could give me a gentle nudge it would be appreciated.

Thanks
 
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This problem is an ideal candidate for the method of "partial fractions".

Try decomposing [tex]\frac{1}{x(x+3)}[/tex] into the form [tex]\frac{A}{x}+\frac{B}{x+3}[/tex] where A and B are constants you need to determine.
 
OH man so obvious. Your the man thank you so much. I havn't had a math class in over a year and now I'm taking diff eq. Bad idea you should definitely keep them all together.
 
And, when talking about functions, be careful to distinguish between "reciprocal" and "inverse" functions!
 

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