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Resolución de integrales/ x^2+1/ 3*x+1/ 13*x/(x^2+13*x+1)

Integral de 13*x/(x^2+13*x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |       13*x       
 |  ------------- dx
 |   2              
 |  x  + 13*x + 1   
 |                  
/                   
0
∫0113x(x2+13x)+1 dx\int\limits_{0}^{1} \frac{13 x}{\left(x^{2} + 13 x\right) + 1}\, dx 
Integral((13*x)/(x^2 + 13*x + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
                              //              /    _____           \                          \                        
                              ||   _____      |2*\/ 165 *(13/2 + x)|                          |                        
                              ||-\/ 165 *acoth|--------------------|                          |                        
  /                           ||              \        165         /                 2        |                        
 |                            ||-------------------------------------  for (13/2 + x)  > 165/4|         /     2       \
 |      13*x                  ||                 330                                          |   13*log\1 + x  + 13*x/
 | ------------- dx = C - 338*|<                                                              | + ---------------------
 |  2                         ||              /    _____           \                          |             2          
 | x  + 13*x + 1              ||   _____      |2*\/ 165 *(13/2 + x)|                          |                        
 |                            ||-\/ 165 *atanh|--------------------|                          |                        
/                             ||              \        165         /                 2        |                        
                              ||-------------------------------------  for (13/2 + x)  < 165/4|                        
                              \\                 330                                          /
∫13x(x2+13x)+1 dx=C−338({−165acoth⁡(2165(x+132)165)330for (x+132)2>1654−165atanh⁡(2165(x+132)165)330for (x+132)2<1654)+13log⁡(x2+13x+1)2\int \frac{13 x}{\left(x^{2} + 13 x\right) + 1}\, dx = C - 338 \left(\begin{cases} - \frac{\sqrt{165} \operatorname{acoth}{\left(\frac{2 \sqrt{165} \left(x + \frac{13}{2}\right)}{165} \right)}}{330} & \text{for}\: \left(x + \frac{13}{2}\right)^{2} > \frac{165}{4} \\- \frac{\sqrt{165} \operatorname{atanh}{\left(\frac{2 \sqrt{165} \left(x + \frac{13}{2}\right)}{165} \right)}}{330} & \text{for}\: \left(x + \frac{13}{2}\right)^{2} < \frac{165}{4} \end{cases}\right) + \frac{13 \log{\left(x^{2} + 13 x + 1 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90050
Trazar el gráfico f(x)
Respuesta [src] 
     /         _____\    /       _____\      /         _____\    /       _____\      /         _____\    /       _____\      /         _____\    /       _____\
     |1   13*\/ 165 |    |13   \/ 165 |      |1   13*\/ 165 |    |13   \/ 165 |      |1   13*\/ 165 |    |15   \/ 165 |      |1   13*\/ 165 |    |15   \/ 165 |
- 13*|- - ----------|*log|-- - -------| - 13*|- + ----------|*log|-- + -------| + 13*|- - ----------|*log|-- - -------| + 13*|- + ----------|*log|-- + -------|
     \2      330    /    \2       2   /      \2      330    /    \2       2   /      \2      330    /    \2       2   /      \2      330    /    \2       2   /
−13(12+13165330)log⁡(1652+132)−13(12−13165330)log⁡(132−1652)+13(12−13165330)log⁡(152−1652)+13(12+13165330)log⁡(1652+152)- 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{13}{2} \right)} - 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{13}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{15}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{15}{2} \right)} 
=
= 
     /         _____\    /       _____\      /         _____\    /       _____\      /         _____\    /       _____\      /         _____\    /       _____\
     |1   13*\/ 165 |    |13   \/ 165 |      |1   13*\/ 165 |    |13   \/ 165 |      |1   13*\/ 165 |    |15   \/ 165 |      |1   13*\/ 165 |    |15   \/ 165 |
- 13*|- - ----------|*log|-- - -------| - 13*|- + ----------|*log|-- + -------| + 13*|- - ----------|*log|-- - -------| + 13*|- + ----------|*log|-- + -------|
     \2      330    /    \2       2   /      \2      330    /    \2       2   /      \2      330    /    \2       2   /      \2      330    /    \2       2   /
−13(12+13165330)log⁡(1652+132)−13(12−13165330)log⁡(132−1652)+13(12−13165330)log⁡(152−1652)+13(12+13165330)log⁡(1652+152)- 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{13}{2} \right)} - 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{13}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{15}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{15}{2} \right)} 
-13*(1/2 - 13*sqrt(165)/330)*log(13/2 - sqrt(165)/2) - 13*(1/2 + 13*sqrt(165)/330)*log(13/2 + sqrt(165)/2) + 13*(1/2 - 13*sqrt(165)/330)*log(15/2 - sqrt(165)/2) + 13*(1/2 + 13*sqrt(165)/330)*log(15/2 + sqrt(165)/2)
Respuesta numérica [src] 
0.768553758891154
0.768553758891154

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

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