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Resolución de integrales/ (5-2x)/ (5-2x)/(x^2-8x-3)

Integral de (5-2x)/(x^2-8x-3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    5 - 2*x      
 |  ------------ dx
 |   2             
 |  x  - 8*x - 3   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{5 - 2 x}{\left(x^{2} - 8 x\right) - 3}\, dx$$ 
Integral((5 - 2*x)/(x^2 - 8*x - 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                //             /  ____         \                     \
                                                ||   ____      |\/ 19 *(-4 + x)|                     |
                                                ||-\/ 19 *acoth|---------------|                     |
  /                                             ||             \       19      /               2     |
 |                                              ||-------------------------------  for (-4 + x)  > 19|
 |   5 - 2*x                /      2      \     ||               19                                  |
 | ------------ dx = C - log\-3 + x  - 8*x/ - 3*|<                                                   |
 |  2                                           ||             /  ____         \                     |
 | x  - 8*x - 3                                 ||   ____      |\/ 19 *(-4 + x)|                     |
 |                                              ||-\/ 19 *atanh|---------------|                     |
/                                               ||             \       19      /               2     |
                                                ||-------------------------------  for (-4 + x)  < 19|
                                                \\               19                                  /
$$\int \frac{5 - 2 x}{\left(x^{2} - 8 x\right) - 3}\, dx = C - 3 \left(\begin{cases} - \frac{\sqrt{19} \operatorname{acoth}{\left(\frac{\sqrt{19} \left(x - 4\right)}{19} \right)}}{19} & \text{for}\: \left(x - 4\right)^{2} > 19 \\- \frac{\sqrt{19} \operatorname{atanh}{\left(\frac{\sqrt{19} \left(x - 4\right)}{19} \right)}}{19} & \text{for}\: \left(x - 4\right)^{2} < 19 \end{cases}\right) - \log{\left(x^{2} - 8 x - 3 \right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
/        ____\                    /        ____\                            /        ____\                    /        ____\                         
|    3*\/ 19 |    /       ____\   |    3*\/ 19 | /          /      ____\\   |    3*\/ 19 |    /       ____\   |    3*\/ 19 | /          /      ____\\
|1 - --------|*log\-4 + \/ 19 / + |1 + --------|*\pi*I + log\4 + \/ 19 // - |1 - --------|*log\-3 + \/ 19 / - |1 + --------|*\pi*I + log\3 + \/ 19 //
\       38   /                    \       38   /                            \       38   /                    \       38   /
$$\left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-4 + \sqrt{19} \right)} - \left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-3 + \sqrt{19} \right)} - \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(3 + \sqrt{19} \right)} + i \pi\right) + \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(4 + \sqrt{19} \right)} + i \pi\right)$$ 
=
= 
/        ____\                    /        ____\                            /        ____\                    /        ____\                         
|    3*\/ 19 |    /       ____\   |    3*\/ 19 | /          /      ____\\   |    3*\/ 19 |    /       ____\   |    3*\/ 19 | /          /      ____\\
|1 - --------|*log\-4 + \/ 19 / + |1 + --------|*\pi*I + log\4 + \/ 19 // - |1 - --------|*log\-3 + \/ 19 / - |1 + --------|*\pi*I + log\3 + \/ 19 //
\       38   /                    \       38   /                            \       38   /                    \       38   /
$$\left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-4 + \sqrt{19} \right)} - \left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-3 + \sqrt{19} \right)} - \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(3 + \sqrt{19} \right)} + i \pi\right) + \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(4 + \sqrt{19} \right)} + i \pi\right)$$ 
(1 - 3*sqrt(19)/38)*log(-4 + sqrt(19)) + (1 + 3*sqrt(19)/38)*(pi*i + log(4 + sqrt(19))) - (1 - 3*sqrt(19)/38)*log(-3 + sqrt(19)) - (1 + 3*sqrt(19)/38)*(pi*i + log(3 + sqrt(19)))
Respuesta numérica [src] 
-0.701963372658831
-0.701963372658831

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

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