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Resolución de integrales/ (x+1)/ (2^x)/ ((2^x)+(3^x))/(6^(x+1))

Integral de ((2^x)+(3^x))/(6^(x+1)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |   x    x   
 |  2  + 3    
 |  ------- dx
 |    x + 1   
 |   6        
 |            
/             
0
∫012x+3x6x+1 dx\int\limits_{0}^{1} \frac{2^{x} + 3^{x}}{6^{x + 1}}\, dx 
Integral((2^x + 3^x)/6^(x + 1), (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901.0-1.0
Trazar el gráfico f(x)
Respuesta [src] 
                               log(2)                                                            log(3)                                                             5*log(6)                                                            2*log(6)                                                            2*log(3)                                                              3*log(2)                             
- --------------------------------------------------------------- - --------------------------------------------------------------- - ------------------------------------------------------------------- + --------------------------------------------------------------- + ------------------------------------------------------------------- + -------------------------------------------------------------------
       2                                                                 2                                                                  2                                                                    2                                                                  2                                                                     2                                                            
  6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)   6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)   36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)   6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)   36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)   36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)
−5log⁡(6)−36log⁡(3)log⁡(6)−36log⁡(2)log⁡(6)+36log⁡(2)log⁡(3)+36log⁡(6)2−log⁡(3)−6log⁡(3)log⁡(6)−6log⁡(2)log⁡(6)+6log⁡(2)log⁡(3)+6log⁡(6)2−log⁡(2)−6log⁡(3)log⁡(6)−6log⁡(2)log⁡(6)+6log⁡(2)log⁡(3)+6log⁡(6)2+3log⁡(2)−36log⁡(3)log⁡(6)−36log⁡(2)log⁡(6)+36log⁡(2)log⁡(3)+36log⁡(6)2+2log⁡(3)−36log⁡(3)log⁡(6)−36log⁡(2)log⁡(6)+36log⁡(2)log⁡(3)+36log⁡(6)2+2log⁡(6)−6log⁡(3)log⁡(6)−6log⁡(2)log⁡(6)+6log⁡(2)log⁡(3)+6log⁡(6)2- \frac{5 \log{\left(6 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} - \frac{\log{\left(3 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} - \frac{\log{\left(2 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} + \frac{3 \log{\left(2 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(3 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(6 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} 
=
= 
                               log(2)                                                            log(3)                                                             5*log(6)                                                            2*log(6)                                                            2*log(3)                                                              3*log(2)                             
- --------------------------------------------------------------- - --------------------------------------------------------------- - ------------------------------------------------------------------- + --------------------------------------------------------------- + ------------------------------------------------------------------- + -------------------------------------------------------------------
       2                                                                 2                                                                  2                                                                    2                                                                  2                                                                     2                                                            
  6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)   6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)   36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)   6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)   36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)   36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)
−5log⁡(6)−36log⁡(3)log⁡(6)−36log⁡(2)log⁡(6)+36log⁡(2)log⁡(3)+36log⁡(6)2−log⁡(3)−6log⁡(3)log⁡(6)−6log⁡(2)log⁡(6)+6log⁡(2)log⁡(3)+6log⁡(6)2−log⁡(2)−6log⁡(3)log⁡(6)−6log⁡(2)log⁡(6)+6log⁡(2)log⁡(3)+6log⁡(6)2+3log⁡(2)−36log⁡(3)log⁡(6)−36log⁡(2)log⁡(6)+36log⁡(2)log⁡(3)+36log⁡(6)2+2log⁡(3)−36log⁡(3)log⁡(6)−36log⁡(2)log⁡(6)+36log⁡(2)log⁡(3)+36log⁡(6)2+2log⁡(6)−6log⁡(3)log⁡(6)−6log⁡(2)log⁡(6)+6log⁡(2)log⁡(3)+6log⁡(6)2- \frac{5 \log{\left(6 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} - \frac{\log{\left(3 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} - \frac{\log{\left(2 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} + \frac{3 \log{\left(2 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(3 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(6 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} 
-log(2)/(6*log(6)^2 - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)) - log(3)/(6*log(6)^2 - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)) - 5*log(6)/(36*log(6)^2 - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)) + 2*log(6)/(6*log(6)^2 - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)) + 2*log(3)/(36*log(6)^2 - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)) + 3*log(2)/(36*log(6)^2 - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3))
Respuesta numérica [src] 
0.221362278588173
0.221362278588173

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

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