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Resolución de integrales/ x^2-5/ 1/((6x^2-5x+1)*log(3/4))

Integral de 1/((6x^2-5x+1)*log(3/4)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                             
  /                             
 |                              
 |              1               
 |  ------------------------- dx
 |  /   2          \            
 |  \6*x  - 5*x + 1/*log(3/4)   
 |                              
/                               
1
$$\int\limits_{1}^{\infty} \frac{1}{\left(\left(6 x^{2} - 5 x\right) + 1\right) \log{\left(\frac{3}{4} \right)}}\, dx$$ 
Integral(1/((6*x^2 - 5*x + 1)*log(3/4)), (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                                                                   
 |                                                                    
 |             1                      -log(-4 + 12*x) + log(-6 + 12*x)
 | ------------------------- dx = C + --------------------------------
 | /   2          \                               log(3/4)            
 | \6*x  - 5*x + 1/*log(3/4)                                          
 |                                                                    
/
$$\int \frac{1}{\left(\left(6 x^{2} - 5 x\right) + 1\right) \log{\left(\frac{3}{4} \right)}}\, dx = C + \frac{\log{\left(12 x - 6 \right)} - \log{\left(12 x - 4 \right)}}{\log{\left(\frac{3}{4} \right)}}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   /7            log(2)                    log(3)        \      /7             log(3)                   log(2)        \
log|-- - ---------------------- + -----------------------|   log|-- - ----------------------- + ----------------------|
   \12   6*(-log(3) + 2*log(2))   12*(-log(3) + 2*log(2))/      \12   12*(-log(3) + 2*log(2))   6*(-log(3) + 2*log(2))/
---------------------------------------------------------- - ----------------------------------------------------------
                    -log(3) + 2*log(2)                                           -log(3) + 2*log(2)
$$\frac{\log{\left(- \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}} - \frac{\log{\left(- \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}}$$ 
=
= 
   /7            log(2)                    log(3)        \      /7             log(3)                   log(2)        \
log|-- - ---------------------- + -----------------------|   log|-- - ----------------------- + ----------------------|
   \12   6*(-log(3) + 2*log(2))   12*(-log(3) + 2*log(2))/      \12   12*(-log(3) + 2*log(2))   6*(-log(3) + 2*log(2))/
---------------------------------------------------------- - ----------------------------------------------------------
                    -log(3) + 2*log(2)                                           -log(3) + 2*log(2)
$$\frac{\log{\left(- \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}} - \frac{\log{\left(- \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}}$$ 
log(7/12 - log(2)/(6*(-log(3) + 2*log(2))) + log(3)/(12*(-log(3) + 2*log(2))))/(-log(3) + 2*log(2)) - log(7/12 - log(3)/(12*(-log(3) + 2*log(2))) + log(2)/(6*(-log(3) + 2*log(2))))/(-log(3) + 2*log(2))

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

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