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Resolución de integrales/ (ln(x)+2)/(x*(1-ln(x)-(ln(x))^2))

Integral de (ln(x)+2)/(x*(1-ln(x)-(ln(x))^2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
  /                            
 |                             
 |         log(x) + 2          
 |  ------------------------ dx
 |    /                2   \   
 |  x*\1 - log(x) - log (x)/   
 |                             
/                              
0
∫01log⁡(x)+2x((1−log⁡(x))−log⁡(x)2) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\left(1 - \log{\left(x \right)}\right) - \log{\left(x \right)}^{2}\right)}\, dx 
Integral((log(x) + 2)/((x*(1 - log(x) - log(x)^2))), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                       //            /    ___               \                            \                             
                                       ||   ___      |2*\/ 5 *(1/2 + log(x))|                            |                             
                                       ||-\/ 5 *acoth|----------------------|                            |                             
  /                                    ||            \          5           /                     2      |                             
 |                                     ||-------------------------------------  for (1/2 + log(x))  > 5/4|      /        2            \
 |        log(x) + 2                   ||                  10                                            |   log\-1 + log (x) + log(x)/
 | ------------------------ dx = C - 6*|<                                                                | - --------------------------
 |   /                2   \            ||            /    ___               \                            |               2             
 | x*\1 - log(x) - log (x)/            ||   ___      |2*\/ 5 *(1/2 + log(x))|                            |                             
 |                                     ||-\/ 5 *atanh|----------------------|                            |                             
/                                      ||            \          5           /                     2      |                             
                                       ||-------------------------------------  for (1/2 + log(x))  < 5/4|                             
                                       \\                  10                                            /
∫log⁡(x)+2x((1−log⁡(x))−log⁡(x)2) dx=C−6({−5acoth⁡(25(log⁡(x)+12)5)10for (log⁡(x)+12)2>54−5atanh⁡(25(log⁡(x)+12)5)10for (log⁡(x)+12)2<54)−log⁡(log⁡(x)2+log⁡(x)−1)2\int \frac{\log{\left(x \right)} + 2}{x \left(\left(1 - \log{\left(x \right)}\right) - \log{\left(x \right)}^{2}\right)}\, dx = C - 6 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(\log{\left(x \right)} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\log{\left(x \right)} + \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(\log{\left(x \right)} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\log{\left(x \right)} + \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) - \frac{\log{\left(\log{\left(x \right)}^{2} + \log{\left(x \right)} - 1 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-50005000
Trazar el gráfico f(x)
Respuesta [src] 
   1                             
   /                             
  |                              
  |          2 + log(x)          
- |  ------------------------- dx
  |    /        2            \   
  |  x*\-1 + log (x) + log(x)/   
  |                              
 /                               
 0
−∫01log⁡(x)+2x(log⁡(x)2+log⁡(x)−1) dx- \int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + \log{\left(x \right)} - 1\right)}\, dx 
=
= 
   1                             
   /                             
  |                              
  |          2 + log(x)          
- |  ------------------------- dx
  |    /        2            \   
  |  x*\-1 + log (x) + log(x)/   
  |                              
 /                               
 0
−∫01log⁡(x)+2x(log⁡(x)2+log⁡(x)−1) dx- \int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + \log{\left(x \right)} - 1\right)}\, dx 
-Integral((2 + log(x))/(x*(-1 + log(x)^2 + log(x))), (x, 0, 1))
Respuesta numérica [src] 
4.28606183812711
4.28606183812711

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

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