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

Integral de 1/(1+6x-x^2) dy

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |             2   
 |  1 + 6*x - x    
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{- x^{2} + \left(6 x + 1\right)}\, dx$$ 
Integral(1/(1 + 6*x - x^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //             /  ____         \                     \
                         ||   ____      |\/ 10 *(-3 + x)|                     |
                         ||-\/ 10 *acoth|---------------|                     |
  /                      ||             \       10      /               2     |
 |                       ||-------------------------------  for (-3 + x)  > 10|
 |      1                ||               10                                  |
 | ------------ dx = C - |<                                                   |
 |            2          ||             /  ____         \                     |
 | 1 + 6*x - x           ||   ____      |\/ 10 *(-3 + x)|                     |
 |                       ||-\/ 10 *atanh|---------------|                     |
/                        ||             \       10      /               2     |
                         ||-------------------------------  for (-3 + x)  < 10|
                         \\               10                                  /
$$\int \frac{1}{- x^{2} + \left(6 x + 1\right)}\, dx = C - \begin{cases} - \frac{\sqrt{10} \operatorname{acoth}{\left(\frac{\sqrt{10} \left(x - 3\right)}{10} \right)}}{10} & \text{for}\: \left(x - 3\right)^{2} > 10 \\- \frac{\sqrt{10} \operatorname{atanh}{\left(\frac{\sqrt{10} \left(x - 3\right)}{10} \right)}}{10} & \text{for}\: \left(x - 3\right)^{2} < 10 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ____ /          /      ____\\     ____    /       ____\     ____ /          /      ____\\     ____    /       ____\
  \/ 10 *\pi*I + log\2 + \/ 10 //   \/ 10 *log\-3 + \/ 10 /   \/ 10 *\pi*I + log\3 + \/ 10 //   \/ 10 *log\-2 + \/ 10 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 20                            20                            20                            20
$$\frac{\sqrt{10} \log{\left(-2 + \sqrt{10} \right)}}{20} - \frac{\sqrt{10} \log{\left(-3 + \sqrt{10} \right)}}{20} - \frac{\sqrt{10} \left(\log{\left(2 + \sqrt{10} \right)} + i \pi\right)}{20} + \frac{\sqrt{10} \left(\log{\left(3 + \sqrt{10} \right)} + i \pi\right)}{20}$$ 
=
= 
    ____ /          /      ____\\     ____    /       ____\     ____ /          /      ____\\     ____    /       ____\
  \/ 10 *\pi*I + log\2 + \/ 10 //   \/ 10 *log\-3 + \/ 10 /   \/ 10 *\pi*I + log\3 + \/ 10 //   \/ 10 *log\-2 + \/ 10 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 20                            20                            20                            20
$$\frac{\sqrt{10} \log{\left(-2 + \sqrt{10} \right)}}{20} - \frac{\sqrt{10} \log{\left(-3 + \sqrt{10} \right)}}{20} - \frac{\sqrt{10} \left(\log{\left(2 + \sqrt{10} \right)} + i \pi\right)}{20} + \frac{\sqrt{10} \left(\log{\left(3 + \sqrt{10} \right)} + i \pi\right)}{20}$$ 
-sqrt(10)*(pi*i + log(2 + sqrt(10)))/20 - sqrt(10)*log(-3 + sqrt(10))/20 + sqrt(10)*(pi*i + log(3 + sqrt(10)))/20 + sqrt(10)*log(-2 + sqrt(10))/20
Respuesta numérica [src] 
0.339296045457796
0.339296045457796

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

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