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

Integral de (x^3)*dx/(√1+2x-x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |          3          
 |         x           
 |  ---------------- dx
 |    ___          2   
 |  \/ 1  + 2*x - x    
 |                     
/                      
0
∫01x3−x2+(2x+1) dx\int\limits_{0}^{1} \frac{x^{3}}{- x^{2} + \left(2 x + \sqrt{1}\right)}\, dx 
Integral(x^3/(sqrt(1) + 2*x - x^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               //            /  ___         \                    \                                  
                               ||   ___      |\/ 2 *(-1 + x)|                    |                                  
  /                            ||-\/ 2 *acoth|--------------|                    |                                  
 |                             ||            \      2       /               2    |                                  
 |         3                   ||-----------------------------  for (-1 + x)  > 2|              /      2      \    2
 |        x                    ||              2                                 |         5*log\-1 + x  - 2*x/   x 
 | ---------------- dx = C - 7*|<                                                | - 2*x - -------------------- - --
 |   ___          2            ||            /  ___         \                    |                  2             2 
 | \/ 1  + 2*x - x             ||   ___      |\/ 2 *(-1 + x)|                    |                                  
 |                             ||-\/ 2 *atanh|--------------|                    |                                  
/                              ||            \      2       /               2    |                                  
                               ||-----------------------------  for (-1 + x)  < 2|                                  
                               \\              2                                 /
∫x3−x2+(2x+1) dx=C−x22−2x−7({−2acoth⁡(2(x−1)2)2for (x−1)2>2−2atanh⁡(2(x−1)2)2for (x−1)2<2)−5log⁡(x2−2x−1)2\int \frac{x^{3}}{- x^{2} + \left(2 x + \sqrt{1}\right)}\, dx = C - \frac{x^{2}}{2} - 2 x - 7 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x - 1\right)}{2} \right)}}{2} & \text{for}\: \left(x - 1\right)^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x - 1\right)}{2} \right)}}{2} & \text{for}\: \left(x - 1\right)^{2} < 2 \end{cases}\right) - \frac{5 \log{\left(x^{2} - 2 x - 1 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Trazar el gráfico f(x)
Respuesta [src] 
      /        ___\                   /        ___\                           /        ___\              /        ___\                    
  5   |5   7*\/ 2 |    /       ___\   |5   7*\/ 2 | /          /      ___\\   |5   7*\/ 2 |    /  ___\   |5   7*\/ 2 | /          /  ___\\
- - + |- - -------|*log\-1 + \/ 2 / + |- + -------|*\pi*I + log\1 + \/ 2 // - |- - -------|*log\\/ 2 / - |- + -------|*\pi*I + log\\/ 2 //
  2   \2      4   /                   \2      4   /                           \2      4   /              \2      4   /
−52+(52−724)log⁡(−1+2)−(52−724)log⁡(2)−(724+52)(log⁡(2)+iπ)+(724+52)(log⁡(1+2)+iπ)- \frac{5}{2} + \left(\frac{5}{2} - \frac{7 \sqrt{2}}{4}\right) \log{\left(-1 + \sqrt{2} \right)} - \left(\frac{5}{2} - \frac{7 \sqrt{2}}{4}\right) \log{\left(\sqrt{2} \right)} - \left(\frac{7 \sqrt{2}}{4} + \frac{5}{2}\right) \left(\log{\left(\sqrt{2} \right)} + i \pi\right) + \left(\frac{7 \sqrt{2}}{4} + \frac{5}{2}\right) \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right) 
=
= 
      /        ___\                   /        ___\                           /        ___\              /        ___\                    
  5   |5   7*\/ 2 |    /       ___\   |5   7*\/ 2 | /          /      ___\\   |5   7*\/ 2 |    /  ___\   |5   7*\/ 2 | /          /  ___\\
- - + |- - -------|*log\-1 + \/ 2 / + |- + -------|*\pi*I + log\1 + \/ 2 // - |- - -------|*log\\/ 2 / - |- + -------|*\pi*I + log\\/ 2 //
  2   \2      4   /                   \2      4   /                           \2      4   /              \2      4   /
−52+(52−724)log⁡(−1+2)−(52−724)log⁡(2)−(724+52)(log⁡(2)+iπ)+(724+52)(log⁡(1+2)+iπ)- \frac{5}{2} + \left(\frac{5}{2} - \frac{7 \sqrt{2}}{4}\right) \log{\left(-1 + \sqrt{2} \right)} - \left(\frac{5}{2} - \frac{7 \sqrt{2}}{4}\right) \log{\left(\sqrt{2} \right)} - \left(\frac{7 \sqrt{2}}{4} + \frac{5}{2}\right) \left(\log{\left(\sqrt{2} \right)} + i \pi\right) + \left(\frac{7 \sqrt{2}}{4} + \frac{5}{2}\right) \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right) 
-5/2 + (5/2 - 7*sqrt(2)/4)*log(-1 + sqrt(2)) + (5/2 + 7*sqrt(2)/4)*(pi*i + log(1 + sqrt(2))) - (5/2 - 7*sqrt(2)/4)*log(sqrt(2)) - (5/2 + 7*sqrt(2)/4)*(pi*i + log(sqrt(2)))
Respuesta numérica [src] 
0.12970872958175
0.12970872958175

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

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