Solving Indefinite Integral: Approach and Techniques

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SUMMARY

The discussion focuses on solving the indefinite integral \(\int\frac{dy}{y(1-y)}\) using the method of partial fractions. Participants emphasize the importance of expressing the integrand as \(\frac{a}{y}+\frac{b}{1-y}\) to determine the constants \(a\) and \(b\). A user mentions their background in differential equations but acknowledges a gap in their knowledge regarding partial fractions. The conversation concludes with a commitment to relearn the method and share the solution.

PREREQUISITES
  • Understanding of indefinite integrals
  • Familiarity with partial fractions decomposition
  • Basic knowledge of algebraic manipulation
  • Experience with differential equations
NEXT STEPS
  • Review the method of partial fractions in calculus
  • Practice solving indefinite integrals using partial fractions
  • Explore applications of partial fractions in differential equations
  • Study advanced integration techniques for complex functions
USEFUL FOR

Students in calculus or differential equations, educators teaching integration techniques, and anyone seeking to strengthen their understanding of partial fractions in mathematical analysis.

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Homework Statement


Solve the indefinite integral


Homework Equations


\int\frac{dy}{y(1-y)}

How do I best approach this problem? I have been stuck for hours!
 
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Use partial fractions. That is write 1/(y(1-y)) as:

<br /> \frac{a}{y}+\frac{b}{1-y}

and determine the constants a and b.
 
Ok, thank you! I am taking a differential equations class but I have forgotten about the method of partial fractions. I will relearn it, and I will post my solution shortly.
 

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