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Resolución de integrales/ x-2^x/ (7^x-2^x)/14^x

Integral de (7^x-2^x)/14^x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0           
  /           
 |            
 |   x    x   
 |  7  - 2    
 |  ------- dx
 |      x     
 |    14      
 |            
/             
-1
$$\int\limits_{-1}^{0} \frac{- 2^{x} + 7^{x}}{14^{x}}\, dx$$ 
Integral((7^x - 2^x)/14^x, (x, -1, 0))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                          log(2)                                                       log(7)                                                           70*log(14)                                                               28*log(2)                                                                98*log(7)                               
---------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------------- - ---------------------------------------------------------------------- + ----------------------------------------------------------------------
   2                                                            2                                                               2                                                                        2                                                                        2                                                               
log (14) + log(2)*log(7) - log(2)*log(14) - log(7)*log(14)   log (14) + log(2)*log(7) - log(2)*log(14) - log(7)*log(14)   14*log (14) - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)   14*log (14) - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)   14*log (14) - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)
$$- \frac{70 \log{\left(14 \right)}}{- 14 \log{\left(7 \right)} \log{\left(14 \right)} - 14 \log{\left(2 \right)} \log{\left(14 \right)} + 14 \log{\left(2 \right)} \log{\left(7 \right)} + 14 \log{\left(14 \right)}^{2}} - \frac{\log{\left(7 \right)}}{- \log{\left(7 \right)} \log{\left(14 \right)} - \log{\left(2 \right)} \log{\left(14 \right)} + \log{\left(2 \right)} \log{\left(7 \right)} + \log{\left(14 \right)}^{2}} - \frac{28 \log{\left(2 \right)}}{- 14 \log{\left(7 \right)} \log{\left(14 \right)} - 14 \log{\left(2 \right)} \log{\left(14 \right)} + 14 \log{\left(2 \right)} \log{\left(7 \right)} + 14 \log{\left(14 \right)}^{2}} + \frac{\log{\left(2 \right)}}{- \log{\left(7 \right)} \log{\left(14 \right)} - \log{\left(2 \right)} \log{\left(14 \right)} + \log{\left(2 \right)} \log{\left(7 \right)} + \log{\left(14 \right)}^{2}} + \frac{98 \log{\left(7 \right)}}{- 14 \log{\left(7 \right)} \log{\left(14 \right)} - 14 \log{\left(2 \right)} \log{\left(14 \right)} + 14 \log{\left(2 \right)} \log{\left(7 \right)} + 14 \log{\left(14 \right)}^{2}}$$ 
=
= 
                          log(2)                                                       log(7)                                                           70*log(14)                                                               28*log(2)                                                                98*log(7)                               
---------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------------- - ---------------------------------------------------------------------- + ----------------------------------------------------------------------
   2                                                            2                                                               2                                                                        2                                                                        2                                                               
log (14) + log(2)*log(7) - log(2)*log(14) - log(7)*log(14)   log (14) + log(2)*log(7) - log(2)*log(14) - log(7)*log(14)   14*log (14) - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)   14*log (14) - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)   14*log (14) - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)
$$- \frac{70 \log{\left(14 \right)}}{- 14 \log{\left(7 \right)} \log{\left(14 \right)} - 14 \log{\left(2 \right)} \log{\left(14 \right)} + 14 \log{\left(2 \right)} \log{\left(7 \right)} + 14 \log{\left(14 \right)}^{2}} - \frac{\log{\left(7 \right)}}{- \log{\left(7 \right)} \log{\left(14 \right)} - \log{\left(2 \right)} \log{\left(14 \right)} + \log{\left(2 \right)} \log{\left(7 \right)} + \log{\left(14 \right)}^{2}} - \frac{28 \log{\left(2 \right)}}{- 14 \log{\left(7 \right)} \log{\left(14 \right)} - 14 \log{\left(2 \right)} \log{\left(14 \right)} + 14 \log{\left(2 \right)} \log{\left(7 \right)} + 14 \log{\left(14 \right)}^{2}} + \frac{\log{\left(2 \right)}}{- \log{\left(7 \right)} \log{\left(14 \right)} - \log{\left(2 \right)} \log{\left(14 \right)} + \log{\left(2 \right)} \log{\left(7 \right)} + \log{\left(14 \right)}^{2}} + \frac{98 \log{\left(7 \right)}}{- 14 \log{\left(7 \right)} \log{\left(14 \right)} - 14 \log{\left(2 \right)} \log{\left(14 \right)} + 14 \log{\left(2 \right)} \log{\left(7 \right)} + 14 \log{\left(14 \right)}^{2}}$$ 
log(2)/(log(14)^2 + log(2)*log(7) - log(2)*log(14) - log(7)*log(14)) - log(7)/(log(14)^2 + log(2)*log(7) - log(2)*log(14) - log(7)*log(14)) - 70*log(14)/(14*log(14)^2 - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)) - 28*log(2)/(14*log(14)^2 - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7)) + 98*log(7)/(14*log(14)^2 - 14*log(2)*log(14) - 14*log(7)*log(14) + 14*log(2)*log(7))
Respuesta numérica [src] 
-1.64069501332954
-1.64069501332954

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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