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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |           2         
 |        6*x          
 |  ---------------- dx
 |       2             
 |  x - x  + 3*x + 2   
 |                     
/                      
0
∫016x2(3x+(−x2+x))+2 dx\int\limits_{0}^{1} \frac{6 x^{2}}{\left(3 x + \left(- x^{2} + x\right)\right) + 2}\, dx 
Integral((6*x^2)/(x - x^2 + 3*x + 2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                //            /  ___         \                    \                              
                                ||   ___      |\/ 6 *(-2 + x)|                    |                              
  /                             ||-\/ 6 *acoth|--------------|                    |                              
 |                              ||            \      6       /               2    |                              
 |          2                   ||-----------------------------  for (-2 + x)  > 6|                              
 |       6*x                    ||              6                                 |         /      2      \      
 | ---------------- dx = C - 60*|<                                                | - 12*log\-2 + x  - 4*x/ - 6*x
 |      2                       ||            /  ___         \                    |                              
 | x - x  + 3*x + 2             ||   ___      |\/ 6 *(-2 + x)|                    |                              
 |                              ||-\/ 6 *atanh|--------------|                    |                              
/                               ||            \      6       /               2    |                              
                                ||-----------------------------  for (-2 + x)  < 6|                              
                                \\              6                                 /
∫6x2(3x+(−x2+x))+2 dx=C−6x−60({−6acoth⁡(6(x−2)6)6for (x−2)2>6−6atanh⁡(6(x−2)6)6for (x−2)2<6)−12log⁡(x2−4x−2)\int \frac{6 x^{2}}{\left(3 x + \left(- x^{2} + x\right)\right) + 2}\, dx = C - 6 x - 60 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} < 6 \end{cases}\right) - 12 \log{\left(x^{2} - 4 x - 2 \right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
       /        ___\                     /        ___\                             /        ___\                     /        ___\                        
       |    5*\/ 6 |    /       ___\     |    5*\/ 6 | /          /      ___\\     |    5*\/ 6 |    /       ___\     |    5*\/ 6 | /          /      ___\\
-6 - 6*|2 - -------|*log\-1 + \/ 6 / - 6*|2 + -------|*\pi*I + log\1 + \/ 6 // + 6*|2 - -------|*log\-2 + \/ 6 / + 6*|2 + -------|*\pi*I + log\2 + \/ 6 //
       \       6   /                     \       6   /                             \       6   /                     \       6   /
−6−6(2−566)log⁡(−1+6)+6(2−566)log⁡(−2+6)−6(2+566)(log⁡(1+6)+iπ)+6(2+566)(log⁡(2+6)+iπ)-6 - 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-1 + \sqrt{6} \right)} + 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-2 + \sqrt{6} \right)} - 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) + 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right) 
=
= 
       /        ___\                     /        ___\                             /        ___\                     /        ___\                        
       |    5*\/ 6 |    /       ___\     |    5*\/ 6 | /          /      ___\\     |    5*\/ 6 |    /       ___\     |    5*\/ 6 | /          /      ___\\
-6 - 6*|2 - -------|*log\-1 + \/ 6 / - 6*|2 + -------|*\pi*I + log\1 + \/ 6 // + 6*|2 - -------|*log\-2 + \/ 6 / + 6*|2 + -------|*\pi*I + log\2 + \/ 6 //
       \       6   /                     \       6   /                             \       6   /                     \       6   /
−6−6(2−566)log⁡(−1+6)+6(2−566)log⁡(−2+6)−6(2+566)(log⁡(1+6)+iπ)+6(2+566)(log⁡(2+6)+iπ)-6 - 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-1 + \sqrt{6} \right)} + 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-2 + \sqrt{6} \right)} - 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) + 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right) 
-6 - 6*(2 - 5*sqrt(6)/6)*log(-1 + sqrt(6)) - 6*(2 + 5*sqrt(6)/6)*(pi*i + log(1 + sqrt(6))) + 6*(2 - 5*sqrt(6)/6)*log(-2 + sqrt(6)) + 6*(2 + 5*sqrt(6)/6)*(pi*i + log(2 + sqrt(6)))
Respuesta numérica [src] 
0.462232123714233
0.462232123714233

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

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