METODO FRACCIONES PARCIALES - UNH - Castañeda

MÉTODO DE FRACCIONES PARCIALES

1. [pic 4]

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Es una fracción propia.

Solución.

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ENTONCES.

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FORMANDO SISTEMA DE ECUACIONES.

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EN 1

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En 2 remplazando 1

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REMPLAZANDO EN 1

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REMPLAZANDO EN LA INTEGRAL.

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Solución

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Solución:

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Resolviendo:

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 [pic 69][pic 70]

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Igualando los coeficientes para sacar las ecuaciones

•   →  (3A+B+C = 0) 4  → 12A+4B+4C=0   ↓(-)[pic 73]
•               → (4B+2C=1)2         →            8B+4C=2[pic 74]
•       →  4B+4C=5    →   4A  4B+4C=5   ↑(-)[pic 75][pic 76][pic 77]

                                               [pic 78][pic 79]

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Resolviendo la integral

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)[pic 96]

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• Factorizamos:

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e)  Resolver:

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Resolución:

• [pic 111]
• [pic 112]

Factorizando el denominador:

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Por tanto nos queda:

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Dividiendo el numerador entre el denominador:[pic 119]

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                         [pic 124][pic 122][pic 123]

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Entonces:

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Hallando  “I”

  =  = [pic 131][pic 132][pic 133]

()[pic 134][pic 135]

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Formando sistema de ecuaciones:

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f) Resolver:

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Resolución:

• [pic 143]
• X[pic 144]

Por lo tanto:

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 F[pic 146][pic 147]

+ [pic 148][pic 149]

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Formando sistema de ecuaciones:

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Solución

   ; Grado: 5[pic 161]

 ; Grado: 7   [pic 162][pic 163][pic 164]

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            +F () +G                                          [pic 169][pic 170][pic 171][pic 172]

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Igualando los coeficientes:

• B+G=0
• [pic 174]
• [pic 175]
• [pic 176]
• [pic 177]
• [pic 178]
•  [pic 179]

Resolviendo la integral:

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h) [pic 184]

solución:

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SISTEMA DE ECUACIONES:

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Solución

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j)

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• [pic 224]

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k) Resolver:

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Resolución:

• [pic 243]
• [pic 244]

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Formando sistema de ecuaciones:

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Entonces:

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factor izamos el denominador aplicando la formula general:

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• [pic 295]

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• [pic 300]

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reemplazamos en la integral:

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Igualando tenemos:

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Entonces tenemos el siguiente sistema de ecuaciones:

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