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Resolución de integrales/ x^2-2/ (1-x)/ 2-2*x/ 2*x+2/ (1-x)/(-x^2-2*x+26)

Integral de (1-x)/(-x^2-2*x+26) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |       1 - x        
 |  --------------- dx
 |     2              
 |  - x  - 2*x + 26   
 |                    
/                     
0
∫011−x(−x2−2x)+26 dx\int\limits_{0}^{1} \frac{1 - x}{\left(- x^{2} - 2 x\right) + 26}\, dx 
Integral((1 - x)/(-x^2 - 2*x + 26), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                   //            /  ___        \                    \
                                                   ||   ___      |\/ 3 *(1 + x)|                    |
                                                   ||-\/ 3 *acoth|-------------|                    |
  /                                                ||            \      9      /              2     |
 |                             /      2      \     ||----------------------------  for (1 + x)  > 27|
 |      1 - x               log\26 - x  - 2*x/     ||             9                                 |
 | --------------- dx = C + ------------------ - 2*|<                                               |
 |    2                             2              ||            /  ___        \                    |
 | - x  - 2*x + 26                                 ||   ___      |\/ 3 *(1 + x)|                    |
 |                                                 ||-\/ 3 *atanh|-------------|                    |
/                                                  ||            \      9      /              2     |
                                                   ||----------------------------  for (1 + x)  < 27|
                                                   \\             9                                 /
∫1−x(−x2−2x)+26 dx=C−2({−3acoth⁡(3(x+1)9)9for (x+1)2>27−3atanh⁡(3(x+1)9)9for (x+1)2<27)+log⁡(−x2−2x+26)2\int \frac{1 - x}{\left(- x^{2} - 2 x\right) + 26}\, dx = C - 2 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \left(x + 1\right)}{9} \right)}}{9} & \text{for}\: \left(x + 1\right)^{2} > 27 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \left(x + 1\right)}{9} \right)}}{9} & \text{for}\: \left(x + 1\right)^{2} < 27 \end{cases}\right) + \frac{\log{\left(- x^{2} - 2 x + 26 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.000.05
Trazar el gráfico f(x)
Respuesta [src] 
/      ___\                              /      ___\                    /      ___\                              /      ___\                 
|1   \/ 3 | /          /         ___\\   |1   \/ 3 |    /        ___\   |1   \/ 3 | /          /         ___\\   |1   \/ 3 |    /        ___\
|- - -----|*\pi*I + log\-2 + 3*\/ 3 // + |- + -----|*log\2 + 3*\/ 3 / - |- - -----|*\pi*I + log\-1 + 3*\/ 3 // - |- + -----|*log\1 + 3*\/ 3 /
\2     9  /                              \2     9  /                    \2     9  /                              \2     9  /
−(39+12)log⁡(1+33)+(39+12)log⁡(2+33)−(12−39)(log⁡(−1+33)+iπ)+(12−39)(log⁡(−2+33)+iπ)- \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(1 + 3 \sqrt{3} \right)} + \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(2 + 3 \sqrt{3} \right)} - \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-1 + 3 \sqrt{3} \right)} + i \pi\right) + \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-2 + 3 \sqrt{3} \right)} + i \pi\right) 
=
= 
/      ___\                              /      ___\                    /      ___\                              /      ___\                 
|1   \/ 3 | /          /         ___\\   |1   \/ 3 |    /        ___\   |1   \/ 3 | /          /         ___\\   |1   \/ 3 |    /        ___\
|- - -----|*\pi*I + log\-2 + 3*\/ 3 // + |- + -----|*log\2 + 3*\/ 3 / - |- - -----|*\pi*I + log\-1 + 3*\/ 3 // - |- + -----|*log\1 + 3*\/ 3 /
\2     9  /                              \2     9  /                    \2     9  /                              \2     9  /
−(39+12)log⁡(1+33)+(39+12)log⁡(2+33)−(12−39)(log⁡(−1+33)+iπ)+(12−39)(log⁡(−2+33)+iπ)- \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(1 + 3 \sqrt{3} \right)} + \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(2 + 3 \sqrt{3} \right)} - \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-1 + 3 \sqrt{3} \right)} + i \pi\right) + \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-2 + 3 \sqrt{3} \right)} + i \pi\right) 
(1/2 - sqrt(3)/9)*(pi*i + log(-2 + 3*sqrt(3))) + (1/2 + sqrt(3)/9)*log(2 + 3*sqrt(3)) - (1/2 - sqrt(3)/9)*(pi*i + log(-1 + 3*sqrt(3))) - (1/2 + sqrt(3)/9)*log(1 + 3*sqrt(3))
Respuesta numérica [src] 
0.0198816522776691
0.0198816522776691

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

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