Integration of Rational Functions by Partial Fractions?

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SUMMARY

The discussion focuses on the integration of rational functions using partial fractions, specifically the equation 5x-13/(x-3)(x-2). The user attempts to decompose the function into partial fractions A/(x-3) + B/(x-2) and reaches a point where they need to equate coefficients. The key step involves identifying coefficients for each power of x from both sides of the equation to solve for A and B. The correct approach is to set up a system of equations based on these coefficients.

PREREQUISITES
  • Understanding of rational functions and their properties
  • Familiarity with partial fraction decomposition techniques
  • Knowledge of polynomial equations and coefficient comparison
  • Basic algebra skills for solving systems of equations
NEXT STEPS
  • Study the method of partial fraction decomposition in detail
  • Learn how to equate coefficients in polynomial equations
  • Practice solving systems of equations to find unknowns
  • Explore integration techniques for rational functions in calculus
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, as well as educators and tutors assisting with rational function integration problems.

black_yurizan
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Integration of Rational Functions by Partial Fractions?

Ok I'm working on some homework problems and I don't even know how to do the first one, here is my problems and the steps that I did thus far ( I don't know if I did them right)

5x-13/(x-3)(x-2)= A/x-3 + B/x-2\rightarrow ...5x-13= A(x-3)(x-2)B(x-2)(x-3)\rightarrow... =(A+B)x2+(-5A-5B)x+(6A+6B)

That's how far I got, I don't know what to do next because in the textbook the next thing they do is equate the coefficients which I don't know how to do and other stuff ...please someone help if you know how to
 
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Well, I'm not entirely sure what you did there, but remember that A+B is the coefficient of x^2, and what's the coefficient of x^2 on the left side of the equation? Then do the same for the other two powers of x.
 


Char. Limit said:
what's the coefficient of x^2 on the left side of the equation?

Sorry, I forgot to put in the x I overlooked that
 

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