Finding Constants for Partial Fraction Integration

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SUMMARY

The discussion focuses on solving the integral ∫(5x^2-3x+1)/((x^2+1)(x-2)) dx using partial fraction decomposition. The user initially struggled with the partial fraction setup and substitution techniques. The correct approach involves expressing the integrand as a sum of simpler fractions: (Ax+B)/(x^2+1) + C/(x-2). The constants A, B, and C must be determined to facilitate integration.

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  • Understanding of integral calculus
  • Familiarity with partial fraction decomposition
  • Knowledge of algebraic manipulation
  • Experience with integration techniques
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  • Practice determining constants in partial fraction decomposition
  • Explore integration techniques for rational functions
  • Learn about the method of residues for complex integrals
  • Review substitution methods in integral calculus
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Students and educators in calculus, mathematicians focusing on integration techniques, and anyone seeking to improve their skills in solving rational integrals.

gordda
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hello, i have the Intergal ∫(5x^2-3x+1)/((x^2+1)(x-2)) dx
i do not know what to do first, i firstly tried to change to partial fraction but that didn't work to, then i tried substitution technique and again i didn't have anything to substitue that got me any further, i don't know what else to try, somebody please help.
thanx:)
 
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Show us your partial fractions work.
 
Determine constants A,B,C so that:
[tex]\frac{5x^{2}-3x+1}{(x^{2}+1)(x-2)}=\frac{Ax+B}{x^{2}+1}+\frac{C}{x-2}[/tex]
 

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