Integrating the Exponential Function with a Polynomial Denominator

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SUMMARY

The discussion focuses on integrating the function (e^x)/((3-e^x)^2). A key technique suggested for solving this integral is the substitution method, specifically using the substitution u = 3 - e^x. This approach simplifies the integration process and allows for a more straightforward calculation of the integral. The exchange highlights the importance of substitution in handling complex integrals involving exponential functions.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with exponential functions
  • Knowledge of substitution methods in integration
  • Basic algebraic manipulation skills
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  • Research advanced integration techniques, focusing on substitution methods
  • Explore integration of exponential functions with polynomial denominators
  • Study the properties of definite and indefinite integrals
  • Practice solving integrals involving complex fractions
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Students and professionals in mathematics, particularly those studying calculus, as well as educators looking for effective methods to teach integration techniques.

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integrate (e^x)/((3-e^x)^2)

thanks very much.
 
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shinkansenfan said:
integrate (e^x)/((3-e^x)^2)

thanks very much.

Try a substitution such as u=3-ex
 
thanks!
 

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