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Resolución de integrales/ (x+3)/ x^2-2/ (x+3)/(x^2-2x-5)

Integral de (x+3)/(x^2-2x-5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |     x + 3       
 |  ------------ dx
 |   2             
 |  x  - 2*x - 5   
 |                 
/                  
0
∫01x+3(x2−2x)−5 dx\int\limits_{0}^{1} \frac{x + 3}{\left(x^{2} - 2 x\right) - 5}\, dx 
Integral((x + 3)/(x^2 - 2*x - 5), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                //            /  ___         \                    \
                                                ||   ___      |\/ 6 *(-1 + x)|                    |
                                                ||-\/ 6 *acoth|--------------|                    |
  /                                             ||            \      6       /               2    |
 |                          /      2      \     ||-----------------------------  for (-1 + x)  > 6|
 |    x + 3              log\-5 + x  - 2*x/     ||              6                                 |
 | ------------ dx = C + ------------------ + 4*|<                                                |
 |  2                            2              ||            /  ___         \                    |
 | x  - 2*x - 5                                 ||   ___      |\/ 6 *(-1 + x)|                    |
 |                                              ||-\/ 6 *atanh|--------------|                    |
/                                               ||            \      6       /               2    |
                                                ||-----------------------------  for (-1 + x)  < 6|
                                                \\              6                                 /
∫x+3(x2−2x)−5 dx=C+4({−6acoth⁡(6(x−1)6)6for (x−1)2>6−6atanh⁡(6(x−1)6)6for (x−1)2<6)+log⁡(x2−2x−5)2\int \frac{x + 3}{\left(x^{2} - 2 x\right) - 5}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 1\right)}{6} \right)}}{6} & \text{for}\: \left(x - 1\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 1\right)}{6} \right)}}{6} & \text{for}\: \left(x - 1\right)^{2} < 6 \end{cases}\right) + \frac{\log{\left(x^{2} - 2 x - 5 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-0.70-0.50
Trazar el gráfico f(x)
Respuesta [src] 
/      ___\              /      ___\                       /      ___\                   /      ___\                        
|1   \/ 6 |    /  ___\   |1   \/ 6 | /          /  ___\\   |1   \/ 6 |    /       ___\   |1   \/ 6 | /          /      ___\\
|- - -----|*log\\/ 6 / + |- + -----|*\pi*I + log\\/ 6 // - |- - -----|*log\-1 + \/ 6 / - |- + -----|*\pi*I + log\1 + \/ 6 //
\2     3  /              \2     3  /                       \2     3  /                   \2     3  /
(12−63)log⁡(6)−(12−63)log⁡(−1+6)−(12+63)(log⁡(1+6)+iπ)+(12+63)(log⁡(6)+iπ)\left(\frac{1}{2} - \frac{\sqrt{6}}{3}\right) \log{\left(\sqrt{6} \right)} - \left(\frac{1}{2} - \frac{\sqrt{6}}{3}\right) \log{\left(-1 + \sqrt{6} \right)} - \left(\frac{1}{2} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{1}{2} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\sqrt{6} \right)} + i \pi\right) 
=
= 
/      ___\              /      ___\                       /      ___\                   /      ___\                        
|1   \/ 6 |    /  ___\   |1   \/ 6 | /          /  ___\\   |1   \/ 6 |    /       ___\   |1   \/ 6 | /          /      ___\\
|- - -----|*log\\/ 6 / + |- + -----|*\pi*I + log\\/ 6 // - |- - -----|*log\-1 + \/ 6 / - |- + -----|*\pi*I + log\1 + \/ 6 //
\2     3  /              \2     3  /                       \2     3  /                   \2     3  /
(12−63)log⁡(6)−(12−63)log⁡(−1+6)−(12+63)(log⁡(1+6)+iπ)+(12+63)(log⁡(6)+iπ)\left(\frac{1}{2} - \frac{\sqrt{6}}{3}\right) \log{\left(\sqrt{6} \right)} - \left(\frac{1}{2} - \frac{\sqrt{6}}{3}\right) \log{\left(-1 + \sqrt{6} \right)} - \left(\frac{1}{2} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{1}{2} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\sqrt{6} \right)} + i \pi\right) 
(1/2 - sqrt(6)/3)*log(sqrt(6)) + (1/2 + sqrt(6)/3)*(pi*i + log(sqrt(6))) - (1/2 - sqrt(6)/3)*log(-1 + sqrt(6)) - (1/2 + sqrt(6)/3)*(pi*i + log(1 + sqrt(6)))
Respuesta numérica [src] 
-0.616753781396557
-0.616753781396557

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

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