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Resolución de integrales/ (4^(x+2)-2^(3x+3)-4+16^x+2^x)/(4^x)

Integral de (4^(x+2)-2^(3x+3)-4+16^x+2^x)/(4^x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                                    
  /                                    
 |                                     
 |   x + 2    3*x + 3         x    x   
 |  4      - 2        - 4 + 16  + 2    
 |  -------------------------------- dx
 |                  x                  
 |                 4                   
 |                                     
/                                      
0
∫022x+(16x+((−23x+3+4x+2)−4))4x dx\int\limits_{0}^{2} \frac{2^{x} + \left(16^{x} + \left(\left(- 2^{3 x + 3} + 4^{x + 2}\right) - 4\right)\right)}{4^{x}}\, dx 
Integral((4^(x + 2) - 2^(3*x + 3) - 4 + 16^x + 2^x)/4^x, (x, 0, 2))
Gráfica
0.02.00.20.40.60.81.01.21.41.61.8-2020
Trazar el gráfico f(x)
Respuesta [src] 
                 log(4)               2*log(4)              -2*log(4)              -log(4)         
                 ------               --------              ---------              --------        
                 log(2)    3           log(2)     3           log(2)     3          log(2)     3   
        13      4      *log (2) - 16*4        *log (2) - 2*4         *log (2) + 4*4        *log (2)
32 + -------- + -----------------------------------------------------------------------------------
     2*log(2)                                             4                                        
                                                     2*log (2)
−16⋅42log⁡(4)log⁡(2)log⁡(2)3−2log⁡(2)342log⁡(4)log⁡(2)+4log⁡(2)34log⁡(4)log⁡(2)+4log⁡(4)log⁡(2)log⁡(2)32log⁡(2)4+132log⁡(2)+32\frac{- 16 \cdot 4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3} - \frac{2 \log{\left(2 \right)}^{3}}{4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}}} + \frac{4 \log{\left(2 \right)}^{3}}{4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}}} + 4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3}}{2 \log{\left(2 \right)}^{4}} + \frac{13}{2 \log{\left(2 \right)}} + 32 
=
= 
                 log(4)               2*log(4)              -2*log(4)              -log(4)         
                 ------               --------              ---------              --------        
                 log(2)    3           log(2)     3           log(2)     3          log(2)     3   
        13      4      *log (2) - 16*4        *log (2) - 2*4         *log (2) + 4*4        *log (2)
32 + -------- + -----------------------------------------------------------------------------------
     2*log(2)                                             4                                        
                                                     2*log (2)
−16⋅42log⁡(4)log⁡(2)log⁡(2)3−2log⁡(2)342log⁡(4)log⁡(2)+4log⁡(2)34log⁡(4)log⁡(2)+4log⁡(4)log⁡(2)log⁡(2)32log⁡(2)4+132log⁡(2)+32\frac{- 16 \cdot 4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3} - \frac{2 \log{\left(2 \right)}^{3}}{4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}}} + \frac{4 \log{\left(2 \right)}^{3}}{4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}}} + 4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3}}{2 \log{\left(2 \right)}^{4}} + \frac{13}{2 \log{\left(2 \right)}} + 32 
32 + 13/(2*log(2)) + (4^(log(4)/log(2))*log(2)^3 - 16*4^(2*log(4)/log(2))*log(2)^3 - 2*4^(-2*log(4)/log(2))*log(2)^3 + 4*4^(-log(4)/log(2))*log(2)^3)/(2*log(2)^4)
Respuesta numérica [src] 
6.57249990433202
6.57249990433202

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

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