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Resolución de integrales/ x^2+9/ dx/(x^2+9*x+7)

Integral de dx/(x^2+9*x+7) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  + 9*x + 7   
 |                 
/                  
0
∫011(x2+9x)+7 dx\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 9 x\right) + 7}\, dx 
Integral(1/(x^2 + 9*x + 7), (x, 0, 1))
Respuesta (Indefinida) [src] 
                           //             /    ____          \                        \
                           ||   ____      |2*\/ 53 *(9/2 + x)|                        |
                           ||-\/ 53 *acoth|------------------|                        |
  /                        ||             \        53        /                2       |
 |                         ||----------------------------------  for (9/2 + x)  > 53/4|
 |      1                  ||               106                                       |
 | ------------ dx = C + 4*|<                                                         |
 |  2                      ||             /    ____          \                        |
 | x  + 9*x + 7            ||   ____      |2*\/ 53 *(9/2 + x)|                        |
 |                         ||-\/ 53 *atanh|------------------|                        |
/                          ||             \        53        /                2       |
                           ||----------------------------------  for (9/2 + x)  < 53/4|
                           \\               106                                       /
∫1(x2+9x)+7 dx=C+4({−53acoth⁡(253(x+92)53)106for (x+92)2>534−53atanh⁡(253(x+92)53)106for (x+92)2<534)\int \frac{1}{\left(x^{2} + 9 x\right) + 7}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{53} \operatorname{acoth}{\left(\frac{2 \sqrt{53} \left(x + \frac{9}{2}\right)}{53} \right)}}{106} & \text{for}\: \left(x + \frac{9}{2}\right)^{2} > \frac{53}{4} \\- \frac{\sqrt{53} \operatorname{atanh}{\left(\frac{2 \sqrt{53} \left(x + \frac{9}{2}\right)}{53} \right)}}{106} & \text{for}\: \left(x + \frac{9}{2}\right)^{2} < \frac{53}{4} \end{cases}\right)
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Trazar el gráfico f(x)
Respuesta [src] 
            /      ____\             /       ____\             /      ____\             /       ____\
    ____    |9   \/ 53 |     ____    |11   \/ 53 |     ____    |9   \/ 53 |     ____    |11   \/ 53 |
  \/ 53 *log|- - ------|   \/ 53 *log|-- + ------|   \/ 53 *log|- + ------|   \/ 53 *log|-- - ------|
            \2     2   /             \2      2   /             \2     2   /             \2      2   /
- ---------------------- - ----------------------- + ---------------------- + -----------------------
            53                        53                       53                        53
−53log⁡(532+112)53−53log⁡(92−532)53+53log⁡(112−532)53+53log⁡(532+92)53- \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{11}{2} \right)}}{53} - \frac{\sqrt{53} \log{\left(\frac{9}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{11}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{9}{2} \right)}}{53} 
=
= 
            /      ____\             /       ____\             /      ____\             /       ____\
    ____    |9   \/ 53 |     ____    |11   \/ 53 |     ____    |9   \/ 53 |     ____    |11   \/ 53 |
  \/ 53 *log|- - ------|   \/ 53 *log|-- + ------|   \/ 53 *log|- + ------|   \/ 53 *log|-- - ------|
            \2     2   /             \2      2   /             \2     2   /             \2      2   /
- ---------------------- - ----------------------- + ---------------------- + -----------------------
            53                        53                       53                        53
−53log⁡(532+112)53−53log⁡(92−532)53+53log⁡(112−532)53+53log⁡(532+92)53- \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{11}{2} \right)}}{53} - \frac{\sqrt{53} \log{\left(\frac{9}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{11}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{9}{2} \right)}}{53} 
-sqrt(53)*log(9/2 - sqrt(53)/2)/53 - sqrt(53)*log(11/2 + sqrt(53)/2)/53 + sqrt(53)*log(9/2 + sqrt(53)/2)/53 + sqrt(53)*log(11/2 - sqrt(53)/2)/53
Respuesta numérica [src] 
0.0900486766096668
0.0900486766096668

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

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