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Resolución de integrales/ 2sinx/ 5cosx/ 1/(5cosx-2sinx)

Integral de 1/(5cosx-2sinx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
 |                        
 |           1            
 |  ------------------- dx
 |  5*cos(x) - 2*sin(x)   
 |                        
/                         
0
∫011−2sin⁡(x)+5cos⁡(x) dx\int\limits_{0}^{1} \frac{1}{- 2 \sin{\left(x \right)} + 5 \cos{\left(x \right)}}\, dx 
Integral(1/(5*cos(x) - 2*sin(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                          /      ____         \             /      ____         \
  /                               ____    |2   \/ 29       /x\|     ____    |2   \/ 29       /x\|
 |                              \/ 29 *log|- - ------ + tan|-||   \/ 29 *log|- + ------ + tan|-||
 |          1                             \5     5         \2//             \5     5         \2//
 | ------------------- dx = C - ------------------------------- + -------------------------------
 | 5*cos(x) - 2*sin(x)                         29                                29              
 |                                                                                               
/
∫1−2sin⁡(x)+5cos⁡(x) dx=C+29log⁡(tan⁡(x2)+25+295)29−29log⁡(tan⁡(x2)−295+25)29\int \frac{1}{- 2 \sin{\left(x \right)} + 5 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{29} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{2}{5} + \frac{\sqrt{29}}{5} \right)}}{29} - \frac{\sqrt{29} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{29}}{5} + \frac{2}{5} \right)}}{29}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Trazar el gráfico f(x)
Respuesta [src] 
         /          /                   ____\\             /      ____\          /          /        ____\\             /      ____           \
    ____ |          |  2              \/ 29 ||     ____    |2   \/ 29 |     ____ |          |  2   \/ 29 ||     ____    |2   \/ 29            |
  \/ 29 *|pi*I + log|- - - tan(1/2) + ------||   \/ 29 *log|- + ------|   \/ 29 *|pi*I + log|- - + ------||   \/ 29 *log|- + ------ + tan(1/2)|
         \          \  5                5   //             \5     5   /          \          \  5     5   //             \5     5              /
- -------------------------------------------- - ---------------------- + --------------------------------- + ---------------------------------
                       29                                  29                             29                                  29
−29log⁡(25+295)29+29log⁡(25+tan⁡(12)+295)29−29(log⁡(−tan⁡(12)−25+295)+iπ)29+29(log⁡(−25+295)+iπ)29- \frac{\sqrt{29} \log{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}}{29} + \frac{\sqrt{29} \log{\left(\frac{2}{5} + \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{29}}{5} \right)}}{29} - \frac{\sqrt{29} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} - \frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{29} + \frac{\sqrt{29} \left(\log{\left(- \frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{29} 
=
= 
         /          /                   ____\\             /      ____\          /          /        ____\\             /      ____           \
    ____ |          |  2              \/ 29 ||     ____    |2   \/ 29 |     ____ |          |  2   \/ 29 ||     ____    |2   \/ 29            |
  \/ 29 *|pi*I + log|- - - tan(1/2) + ------||   \/ 29 *log|- + ------|   \/ 29 *|pi*I + log|- - + ------||   \/ 29 *log|- + ------ + tan(1/2)|
         \          \  5                5   //             \5     5   /          \          \  5     5   //             \5     5              /
- -------------------------------------------- - ---------------------- + --------------------------------- + ---------------------------------
                       29                                  29                             29                                  29
−29log⁡(25+295)29+29log⁡(25+tan⁡(12)+295)29−29(log⁡(−tan⁡(12)−25+295)+iπ)29+29(log⁡(−25+295)+iπ)29- \frac{\sqrt{29} \log{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}}{29} + \frac{\sqrt{29} \log{\left(\frac{2}{5} + \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{29}}{5} \right)}}{29} - \frac{\sqrt{29} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} - \frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{29} + \frac{\sqrt{29} \left(\log{\left(- \frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{29} 
-sqrt(29)*(pi*i + log(-2/5 - tan(1/2) + sqrt(29)/5))/29 - sqrt(29)*log(2/5 + sqrt(29)/5)/29 + sqrt(29)*(pi*i + log(-2/5 + sqrt(29)/5))/29 + sqrt(29)*log(2/5 + sqrt(29)/5 + tan(1/2))/29
Respuesta numérica [src] 
0.363831811633876
0.363831811633876

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

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