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Resolución de integrales/ sin(x)/ cos(x)/ 1/(7sin(x)+9cos(x)+2)

Integral de 1/(7sin(x)+9cos(x)+2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                           
  /                           
 |                            
 |             1              
 |  ----------------------- dx
 |  7*sin(x) + 9*cos(x) + 2   
 |                            
/                             
0
∫011(7sin⁡(x)+9cos⁡(x))+2 dx\int\limits_{0}^{1} \frac{1}{\left(7 \sin{\left(x \right)} + 9 \cos{\left(x \right)}\right) + 2}\, dx 
Integral(1/(7*sin(x) + 9*cos(x) + 2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                              /         ____         \             /         ____         \
  /                                   ____    |     3*\/ 14       /x\|     ____    |     3*\/ 14       /x\|
 |                                  \/ 14 *log|-1 - -------- + tan|-||   \/ 14 *log|-1 + -------- + tan|-||
 |            1                               \        7          \2//             \        7          \2//
 | ----------------------- dx = C - ---------------------------------- + ----------------------------------
 | 7*sin(x) + 9*cos(x) + 2                          42                                   42                
 |                                                                                                         
/
∫1(7sin⁡(x)+9cos⁡(x))+2 dx=C+14log⁡(tan⁡(x2)−1+3147)42−14log⁡(tan⁡(x2)−3147−1)42\int \frac{1}{\left(7 \sin{\left(x \right)} + 9 \cos{\left(x \right)}\right) + 2}\, dx = C + \frac{\sqrt{14} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3 \sqrt{14}}{7} - 1 \right)}}{42}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.060.10
Trazar el gráfico f(x)
Respuesta [src] 
         /          /                   ____\\             /         ____\          /          /        ____\\             /         ____           \
    ____ |          |               3*\/ 14 ||     ____    |     3*\/ 14 |     ____ |          |    3*\/ 14 ||     ____    |     3*\/ 14            |
  \/ 14 *|pi*I + log|1 - tan(1/2) + --------||   \/ 14 *log|-1 + --------|   \/ 14 *|pi*I + log|1 + --------||   \/ 14 *log|-1 + -------- + tan(1/2)|
         \          \                  7    //             \        7    /          \          \       7    //             \        7               /
- -------------------------------------------- - ------------------------- + --------------------------------- + ------------------------------------
                       42                                    42                              42                                   42
14log⁡(−1+tan⁡(12)+3147)42−14log⁡(−1+3147)42−14(log⁡(−tan⁡(12)+1+3147)+iπ)42+14(log⁡(1+3147)+iπ)42\frac{\sqrt{14} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \log{\left(-1 + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42} + \frac{\sqrt{14} \left(\log{\left(1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42} 
=
= 
         /          /                   ____\\             /         ____\          /          /        ____\\             /         ____           \
    ____ |          |               3*\/ 14 ||     ____    |     3*\/ 14 |     ____ |          |    3*\/ 14 ||     ____    |     3*\/ 14            |
  \/ 14 *|pi*I + log|1 - tan(1/2) + --------||   \/ 14 *log|-1 + --------|   \/ 14 *|pi*I + log|1 + --------||   \/ 14 *log|-1 + -------- + tan(1/2)|
         \          \                  7    //             \        7    /          \          \       7    //             \        7               /
- -------------------------------------------- - ------------------------- + --------------------------------- + ------------------------------------
                       42                                    42                              42                                   42
14log⁡(−1+tan⁡(12)+3147)42−14log⁡(−1+3147)42−14(log⁡(−tan⁡(12)+1+3147)+iπ)42+14(log⁡(1+3147)+iπ)42\frac{\sqrt{14} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \log{\left(-1 + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42} + \frac{\sqrt{14} \left(\log{\left(1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42} 
-sqrt(14)*(pi*i + log(1 - tan(1/2) + 3*sqrt(14)/7))/42 - sqrt(14)*log(-1 + 3*sqrt(14)/7)/42 + sqrt(14)*(pi*i + log(1 + 3*sqrt(14)/7))/42 + sqrt(14)*log(-1 + 3*sqrt(14)/7 + tan(1/2))/42
Respuesta numérica [src] 
0.0784012196748086
0.0784012196748086

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

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