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Resolución de integrales/ ((2^x)/(log(2)/log(10)))*(-3*sin(3x))

Integral de ((2^x)/(log(2)/log(10)))*(-3*sin(3x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |       x                  
 |      2                   
 |  ---------*-3*sin(3*x) dx
 |  / log(2)\               
 |  |-------|               
 |  \log(10)/               
 |                          
/                           
0
∫012xlog⁡(2)1log⁡(10)(−3sin⁡(3x)) dx\int\limits_{0}^{1} \frac{2^{x}}{\log{\left(2 \right)} \frac{1}{\log{\left(10 \right)}}} \left(- 3 \sin{\left(3 x \right)}\right)\, dx 
Integral((2^x/((log(2)/log(10))))*(-3*sin(3*x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                    /     x             x                \        
  /                                 |  3*2 *cos(3*x)   2 *log(2)*sin(3*x)|        
 |                                3*|- ------------- + ------------------|*log(10)
 |      x                           |          2                 2       |        
 |     2                            \   9 + log (2)       9 + log (2)    /        
 | ---------*-3*sin(3*x) dx = C - ------------------------------------------------
 | / log(2)\                                           log(2)                     
 | |-------|                                                                      
 | \log(10)/                                                                      
 |                                                                                
/
∫2xlog⁡(2)1log⁡(10)(−3sin⁡(3x)) dx=C−3(2xlog⁡(2)sin⁡(3x)log⁡(2)2+9−3⋅2xcos⁡(3x)log⁡(2)2+9)log⁡(10)log⁡(2)\int \frac{2^{x}}{\log{\left(2 \right)} \frac{1}{\log{\left(10 \right)}}} \left(- 3 \sin{\left(3 x \right)}\right)\, dx = C - \frac{3 \left(\frac{2^{x} \log{\left(2 \right)} \sin{\left(3 x \right)}}{\log{\left(2 \right)}^{2} + 9} - \frac{3 \cdot 2^{x} \cos{\left(3 x \right)}}{\log{\left(2 \right)}^{2} + 9}\right) \log{\left(10 \right)}}{\log{\left(2 \right)}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-2020
Trazar el gráfico f(x)
Respuesta [src] 
                           /    6*cos(3)    2*log(2)*sin(3)\        
                         3*|- ----------- + ---------------|*log(10)
                           |         2               2     |        
       9*log(10)           \  9 + log (2)     9 + log (2)  /        
- -------------------- - -------------------------------------------
  /       2   \                             log(2)                  
  \9 + log (2)/*log(2)
−3(2log⁡(2)sin⁡(3)log⁡(2)2+9−6cos⁡(3)log⁡(2)2+9)log⁡(10)log⁡(2)−9log⁡(10)(log⁡(2)2+9)log⁡(2)- \frac{3 \left(\frac{2 \log{\left(2 \right)} \sin{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9} - \frac{6 \cos{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9}\right) \log{\left(10 \right)}}{\log{\left(2 \right)}} - \frac{9 \log{\left(10 \right)}}{\left(\log{\left(2 \right)}^{2} + 9\right) \log{\left(2 \right)}} 
=
= 
                           /    6*cos(3)    2*log(2)*sin(3)\        
                         3*|- ----------- + ---------------|*log(10)
                           |         2               2     |        
       9*log(10)           \  9 + log (2)     9 + log (2)  /        
- -------------------- - -------------------------------------------
  /       2   \                             log(2)                  
  \9 + log (2)/*log(2)
−3(2log⁡(2)sin⁡(3)log⁡(2)2+9−6cos⁡(3)log⁡(2)2+9)log⁡(10)log⁡(2)−9log⁡(10)(log⁡(2)2+9)log⁡(2)- \frac{3 \left(\frac{2 \log{\left(2 \right)} \sin{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9} - \frac{6 \cos{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9}\right) \log{\left(10 \right)}}{\log{\left(2 \right)}} - \frac{9 \log{\left(10 \right)}}{\left(\log{\left(2 \right)}^{2} + 9\right) \log{\left(2 \right)}} 
-9*log(10)/((9 + log(2)^2)*log(2)) - 3*(-6*cos(3)/(9 + log(2)^2) + 2*log(2)*sin(3)/(9 + log(2)^2))*log(10)/log(2)
Respuesta numérica [src] 
-9.60326554743131
-9.60326554743131

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

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