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Resolución de integrales/ dx/(x^2+6*x+7)

Integral de dx/(x^2+6*x+7) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  + 6*x + 7   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 6 x\right) + 7}\, dx$$ 
Integral(1/(x^2 + 6*x + 7), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //            /  ___        \                   \
                         ||   ___      |\/ 2 *(3 + x)|                   |
                         ||-\/ 2 *acoth|-------------|                   |
  /                      ||            \      2      /              2    |
 |                       ||----------------------------  for (3 + x)  > 2|
 |      1                ||             2                                |
 | ------------ dx = C + |<                                              |
 |  2                    ||            /  ___        \                   |
 | x  + 6*x + 7          ||   ___      |\/ 2 *(3 + x)|                   |
 |                       ||-\/ 2 *atanh|-------------|                   |
/                        ||            \      2      /              2    |
                         ||----------------------------  for (3 + x)  < 2|
                         \\             2                                /
$$\int \frac{1}{\left(x^{2} + 6 x\right) + 7}\, dx = C + \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x + 3\right)}{2} \right)}}{2} & \text{for}\: \left(x + 3\right)^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x + 3\right)}{2} \right)}}{2} & \text{for}\: \left(x + 3\right)^{2} < 2 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ___    /      ___\     ___    /      ___\     ___    /      ___\     ___    /      ___\
  \/ 2 *log\3 - \/ 2 /   \/ 2 *log\4 + \/ 2 /   \/ 2 *log\3 + \/ 2 /   \/ 2 *log\4 - \/ 2 /
- -------------------- - -------------------- + -------------------- + --------------------
           4                      4                      4                      4
$$- \frac{\sqrt{2} \log{\left(\sqrt{2} + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(3 - \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \log{\left(4 - \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \log{\left(\sqrt{2} + 3 \right)}}{4}$$ 
=
= 
    ___    /      ___\     ___    /      ___\     ___    /      ___\     ___    /      ___\
  \/ 2 *log\3 - \/ 2 /   \/ 2 *log\4 + \/ 2 /   \/ 2 *log\3 + \/ 2 /   \/ 2 *log\4 - \/ 2 /
- -------------------- - -------------------- + -------------------- + --------------------
           4                      4                      4                      4
$$- \frac{\sqrt{2} \log{\left(\sqrt{2} + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(3 - \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \log{\left(4 - \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \log{\left(\sqrt{2} + 3 \right)}}{4}$$ 
-sqrt(2)*log(3 - sqrt(2))/4 - sqrt(2)*log(4 + sqrt(2))/4 + sqrt(2)*log(3 + sqrt(2))/4 + sqrt(2)*log(4 - sqrt(2))/4
Respuesta numérica [src] 
0.100674782759751
0.100674782759751

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

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