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Resolución de integrales/ (x-2)/ (x-1)/ (x-1)*5^(x-2)/6^x

Integral de (x-1)*5^(x-2)/6^x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3                  
  /                  
 |                   
 |           x - 2   
 |  (x - 1)*5        
 |  -------------- dx
 |         x         
 |        6          
 |                   
/                    
0
∫035x−2(x−1)6x dx\int\limits_{0}^{3} \frac{5^{x - 2} \left(x - 1\right)}{6^{x}}\, dx 
Integral(((x - 1)*5^(x - 2))/6^x, (x, 0, 3))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                              
 |                                                                                                                                                                                                               
 |          x - 2                       x                                        x                                                x                                                   x                          
 | (x - 1)*5                           5                                        5                                              x*5 *log(6)                                         x*5 *log(5)                   
 | -------------- dx = C - -------------------------- - ------------------------------------------------- - ------------------------------------------------- + -------------------------------------------------
 |        x                   / x           x       \      / x    2       x    2         x              \      / x    2       x    2         x              \      / x    2       x    2         x              \
 |       6                 25*\6 *log(5) - 6 *log(6)/   25*\6 *log (5) + 6 *log (6) - 2*6 *log(5)*log(6)/   25*\6 *log (5) + 6 *log (6) - 2*6 *log(5)*log(6)/   25*\6 *log (5) + 6 *log (6) - 2*6 *log(5)*log(6)/
 |                                                                                                                                                                                                               
/
∫5x−2(x−1)6x dx=−5xxlog⁡(6)25(−2⋅6xlog⁡(5)log⁡(6)+6xlog⁡(5)2+6xlog⁡(6)2)+5xxlog⁡(5)25(−2⋅6xlog⁡(5)log⁡(6)+6xlog⁡(5)2+6xlog⁡(6)2)−5x25(−2⋅6xlog⁡(5)log⁡(6)+6xlog⁡(5)2+6xlog⁡(6)2)−5x25(−6xlog⁡(6)+6xlog⁡(5))+C\int \frac{5^{x - 2} \left(x - 1\right)}{6^{x}}\, dx = - \frac{5^{x} x \log{\left(6 \right)}}{25 \left(- 2 \cdot 6^{x} \log{\left(5 \right)} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}^{2} + 6^{x} \log{\left(6 \right)}^{2}\right)} + \frac{5^{x} x \log{\left(5 \right)}}{25 \left(- 2 \cdot 6^{x} \log{\left(5 \right)} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}^{2} + 6^{x} \log{\left(6 \right)}^{2}\right)} - \frac{5^{x}}{25 \left(- 2 \cdot 6^{x} \log{\left(5 \right)} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}^{2} + 6^{x} \log{\left(6 \right)}^{2}\right)} - \frac{5^{x}}{25 \left(- 6^{x} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}\right)} + C
Simplificar
Gráfica
0.003.000.250.500.751.001.251.501.752.002.252.502.751-2
Trazar el gráfico f(x)
Respuesta [src] 
                    1                                               125                                            log(5)                                       log(6)                                         250*log(6)                                          250*log(5)                   
------------------------------------------ - ------------------------------------------------- + ------------------------------------------ - ------------------------------------------ - ------------------------------------------------- + -------------------------------------------------
      2            2                                 2              2                                  2            2                               2            2                                 2              2                                    2              2                         
25*log (5) + 25*log (6) - 50*log(5)*log(6)   5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)   25*log (5) + 25*log (6) - 50*log(5)*log(6)   25*log (5) + 25*log (6) - 50*log(5)*log(6)   5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)   5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)
−250log⁡(6)−10800log⁡(5)log⁡(6)+5400log⁡(5)2+5400log⁡(6)2−log⁡(6)−50log⁡(5)log⁡(6)+25log⁡(5)2+25log⁡(6)2−125−10800log⁡(5)log⁡(6)+5400log⁡(5)2+5400log⁡(6)2+1−50log⁡(5)log⁡(6)+25log⁡(5)2+25log⁡(6)2+log⁡(5)−50log⁡(5)log⁡(6)+25log⁡(5)2+25log⁡(6)2+250log⁡(5)−10800log⁡(5)log⁡(6)+5400log⁡(5)2+5400log⁡(6)2- \frac{250 \log{\left(6 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} - \frac{\log{\left(6 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} - \frac{125}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} + \frac{1}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{\log{\left(5 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{250 \log{\left(5 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} 
=
= 
                    1                                               125                                            log(5)                                       log(6)                                         250*log(6)                                          250*log(5)                   
------------------------------------------ - ------------------------------------------------- + ------------------------------------------ - ------------------------------------------ - ------------------------------------------------- + -------------------------------------------------
      2            2                                 2              2                                  2            2                               2            2                                 2              2                                    2              2                         
25*log (5) + 25*log (6) - 50*log(5)*log(6)   5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)   25*log (5) + 25*log (6) - 50*log(5)*log(6)   25*log (5) + 25*log (6) - 50*log(5)*log(6)   5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)   5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)
−250log⁡(6)−10800log⁡(5)log⁡(6)+5400log⁡(5)2+5400log⁡(6)2−log⁡(6)−50log⁡(5)log⁡(6)+25log⁡(5)2+25log⁡(6)2−125−10800log⁡(5)log⁡(6)+5400log⁡(5)2+5400log⁡(6)2+1−50log⁡(5)log⁡(6)+25log⁡(5)2+25log⁡(6)2+log⁡(5)−50log⁡(5)log⁡(6)+25log⁡(5)2+25log⁡(6)2+250log⁡(5)−10800log⁡(5)log⁡(6)+5400log⁡(5)2+5400log⁡(6)2- \frac{250 \log{\left(6 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} - \frac{\log{\left(6 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} - \frac{125}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} + \frac{1}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{\log{\left(5 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{250 \log{\left(5 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} 
1/(25*log(5)^2 + 25*log(6)^2 - 50*log(5)*log(6)) - 125/(5400*log(5)^2 + 5400*log(6)^2 - 10800*log(5)*log(6)) + log(5)/(25*log(5)^2 + 25*log(6)^2 - 50*log(5)*log(6)) - log(6)/(25*log(5)^2 + 25*log(6)^2 - 50*log(5)*log(6)) - 250*log(6)/(5400*log(5)^2 + 5400*log(6)^2 - 10800*log(5)*log(6)) + 250*log(5)/(5400*log(5)^2 + 5400*log(6)^2 - 10800*log(5)*log(6))
Respuesta numérica [src] 
0.0336383296951058
0.0336383296951058

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

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