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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |   -x /     x - 1\   
 |  2  *\6 + 3     / dx
 |                     
/                      
0
∫012−x(3x−1+6) dx\int\limits_{0}^{1} 2^{- x} \left(3^{x - 1} + 6\right)\, dx 
Integral(2^(-x)*(6 + 3^(x - 1)), (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-2020
Trazar el gráfico f(x)
Respuesta [src] 
           21*log(2)                     18*log(3)                     18*log(3)                     19*log(2)         
- --------------------------- - --------------------------- + --------------------------- + ---------------------------
       2                             2                             2                             2                     
  6*log (2) - 6*log(2)*log(3)   3*log (2) - 3*log(2)*log(3)   6*log (2) - 6*log(2)*log(3)   3*log (2) - 3*log(2)*log(3)
19log⁡(2)−3log⁡(2)log⁡(3)+3log⁡(2)2+18log⁡(3)−6log⁡(2)log⁡(3)+6log⁡(2)2−21log⁡(2)−6log⁡(2)log⁡(3)+6log⁡(2)2−18log⁡(3)−3log⁡(2)log⁡(3)+3log⁡(2)2\frac{19 \log{\left(2 \right)}}{- 3 \log{\left(2 \right)} \log{\left(3 \right)} + 3 \log{\left(2 \right)}^{2}} + \frac{18 \log{\left(3 \right)}}{- 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(2 \right)}^{2}} - \frac{21 \log{\left(2 \right)}}{- 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(2 \right)}^{2}} - \frac{18 \log{\left(3 \right)}}{- 3 \log{\left(2 \right)} \log{\left(3 \right)} + 3 \log{\left(2 \right)}^{2}} 
=
= 
           21*log(2)                     18*log(3)                     18*log(3)                     19*log(2)         
- --------------------------- - --------------------------- + --------------------------- + ---------------------------
       2                             2                             2                             2                     
  6*log (2) - 6*log(2)*log(3)   3*log (2) - 3*log(2)*log(3)   6*log (2) - 6*log(2)*log(3)   3*log (2) - 3*log(2)*log(3)
19log⁡(2)−3log⁡(2)log⁡(3)+3log⁡(2)2+18log⁡(3)−6log⁡(2)log⁡(3)+6log⁡(2)2−21log⁡(2)−6log⁡(2)log⁡(3)+6log⁡(2)2−18log⁡(3)−3log⁡(2)log⁡(3)+3log⁡(2)2\frac{19 \log{\left(2 \right)}}{- 3 \log{\left(2 \right)} \log{\left(3 \right)} + 3 \log{\left(2 \right)}^{2}} + \frac{18 \log{\left(3 \right)}}{- 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(2 \right)}^{2}} - \frac{21 \log{\left(2 \right)}}{- 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(2 \right)}^{2}} - \frac{18 \log{\left(3 \right)}}{- 3 \log{\left(2 \right)} \log{\left(3 \right)} + 3 \log{\left(2 \right)}^{2}} 
-21*log(2)/(6*log(2)^2 - 6*log(2)*log(3)) - 18*log(3)/(3*log(2)^2 - 3*log(2)*log(3)) + 18*log(3)/(6*log(2)^2 - 6*log(2)*log(3)) + 19*log(2)/(3*log(2)^2 - 3*log(2)*log(3))
Respuesta numérica [src] 
4.73913569972963
4.73913569972963

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

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