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Resolución de integrales/ 6*x^2/ x^2/(7-6*x^2)

Integral de x^2/(7-6*x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |      2      
 |     x       
 |  -------- dx
 |         2   
 |  7 - 6*x    
 |             
/              
0
∫01x27−6x2 dx\int\limits_{0}^{1} \frac{x^{2}}{7 - 6 x^{2}}\, dx 
Integral(x^2/(7 - 6*x^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                       //             /    ____\               \    
                       ||   ____      |x*\/ 42 |               |    
                       ||-\/ 42 *acoth|--------|               |    
                       ||             \   7    /        2      |    
                       ||------------------------  for x  > 7/6|    
                       ||           42                         |    
                     7*|<                                      |    
                       ||             /    ____\               |    
                       ||   ____      |x*\/ 42 |               |    
  /                    ||-\/ 42 *atanh|--------|               |    
 |                     ||             \   7    /        2      |    
 |     2               ||------------------------  for x  < 7/6|    
 |    x                \\           42                         /   x
 | -------- dx = C - ------------------------------------------- - -
 |        2                               6                        6
 | 7 - 6*x                                                          
 |                                                                  
/
∫x27−6x2 dx=C−x6−7({−42acoth⁡(42x7)42for x2>76−42atanh⁡(42x7)42for x2<76)6\int \frac{x^{2}}{7 - 6 x^{2}}\, dx = C - \frac{x}{6} - \frac{7 \left(\begin{cases} - \frac{\sqrt{42} \operatorname{acoth}{\left(\frac{\sqrt{42} x}{7} \right)}}{42} & \text{for}\: x^{2} > \frac{7}{6} \\- \frac{\sqrt{42} \operatorname{atanh}{\left(\frac{\sqrt{42} x}{7} \right)}}{42} & \text{for}\: x^{2} < \frac{7}{6} \end{cases}\right)}{6}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
             /          /       ____\\             /  ____\          /          /  ____\\             /      ____\
        ____ |          |     \/ 42 ||     ____    |\/ 42 |     ____ |          |\/ 42 ||     ____    |    \/ 42 |
      \/ 42 *|pi*I + log|-1 + ------||   \/ 42 *log|------|   \/ 42 *|pi*I + log|------||   \/ 42 *log|1 + ------|
  1          \          \       6   //             \  6   /          \          \  6   //             \      6   /
- - - -------------------------------- - ------------------ + --------------------------- + ----------------------
  6                  72                          72                        72                         72
−16−42log⁡(426)72+42log⁡(1+426)72−42(log⁡(−1+426)+iπ)72+42(log⁡(426)+iπ)72- \frac{1}{6} - \frac{\sqrt{42} \log{\left(\frac{\sqrt{42}}{6} \right)}}{72} + \frac{\sqrt{42} \log{\left(1 + \frac{\sqrt{42}}{6} \right)}}{72} - \frac{\sqrt{42} \left(\log{\left(-1 + \frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72} + \frac{\sqrt{42} \left(\log{\left(\frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72} 
=
= 
             /          /       ____\\             /  ____\          /          /  ____\\             /      ____\
        ____ |          |     \/ 42 ||     ____    |\/ 42 |     ____ |          |\/ 42 ||     ____    |    \/ 42 |
      \/ 42 *|pi*I + log|-1 + ------||   \/ 42 *log|------|   \/ 42 *|pi*I + log|------||   \/ 42 *log|1 + ------|
  1          \          \       6   //             \  6   /          \          \  6   //             \      6   /
- - - -------------------------------- - ------------------ + --------------------------- + ----------------------
  6                  72                          72                        72                         72
−16−42log⁡(426)72+42log⁡(1+426)72−42(log⁡(−1+426)+iπ)72+42(log⁡(426)+iπ)72- \frac{1}{6} - \frac{\sqrt{42} \log{\left(\frac{\sqrt{42}}{6} \right)}}{72} + \frac{\sqrt{42} \log{\left(1 + \frac{\sqrt{42}}{6} \right)}}{72} - \frac{\sqrt{42} \left(\log{\left(-1 + \frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72} + \frac{\sqrt{42} \left(\log{\left(\frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72} 
-1/6 - sqrt(42)*(pi*i + log(-1 + sqrt(42)/6))/72 - sqrt(42)*log(sqrt(42)/6)/72 + sqrt(42)*(pi*i + log(sqrt(42)/6))/72 + sqrt(42)*log(1 + sqrt(42)/6)/72
Respuesta numérica [src] 
0.126462091609384
0.126462091609384

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

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