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Resolución de integrales/ cos(x)/ sin(x)/ 1/(6+8sin(x)+5cos(x))

Integral de 1/(6+8sin(x)+5cos(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                           
  /                           
 |                            
 |             1              
 |  ----------------------- dx
 |  6 + 8*sin(x) + 5*cos(x)   
 |                            
/                             
0
$$\int\limits_{0}^{1} \frac{1}{\left(8 \sin{\left(x \right)} + 6\right) + 5 \cos{\left(x \right)}}\, dx$$ 
Integral(1/(6 + 8*sin(x) + 5*cos(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                   ____    /      ____      /x\\     ____    /      ____      /x\\
 |                                  \/ 53 *log|8 + \/ 53  + tan|-||   \/ 53 *log|8 - \/ 53  + tan|-||
 |            1                               \                \2//             \                \2//
 | ----------------------- dx = C - ------------------------------- + -------------------------------
 | 6 + 8*sin(x) + 5*cos(x)                         53                                53              
 |                                                                                                   
/
$$\int \frac{1}{\left(8 \sin{\left(x \right)} + 6\right) + 5 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{53} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{53} + 8 \right)}}{53} - \frac{\sqrt{53} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{53} + 8 \right)}}{53}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ____    /      ____\     ____    /      ____           \     ____    /      ____\     ____    /      ____           \
  \/ 53 *log\8 - \/ 53 /   \/ 53 *log\8 + \/ 53  + tan(1/2)/   \/ 53 *log\8 + \/ 53 /   \/ 53 *log\8 - \/ 53  + tan(1/2)/
- ---------------------- - --------------------------------- + ---------------------- + ---------------------------------
            53                             53                            53                             53
$$- \frac{\sqrt{53} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{53} + 8 \right)}}{53} + \frac{\sqrt{53} \log{\left(- \sqrt{53} + \tan{\left(\frac{1}{2} \right)} + 8 \right)}}{53} - \frac{\sqrt{53} \log{\left(8 - \sqrt{53} \right)}}{53} + \frac{\sqrt{53} \log{\left(\sqrt{53} + 8 \right)}}{53}$$ 
=
= 
    ____    /      ____\     ____    /      ____           \     ____    /      ____\     ____    /      ____           \
  \/ 53 *log\8 - \/ 53 /   \/ 53 *log\8 + \/ 53  + tan(1/2)/   \/ 53 *log\8 + \/ 53 /   \/ 53 *log\8 - \/ 53  + tan(1/2)/
- ---------------------- - --------------------------------- + ---------------------- + ---------------------------------
            53                             53                            53                             53
$$- \frac{\sqrt{53} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{53} + 8 \right)}}{53} + \frac{\sqrt{53} \log{\left(- \sqrt{53} + \tan{\left(\frac{1}{2} \right)} + 8 \right)}}{53} - \frac{\sqrt{53} \log{\left(8 - \sqrt{53} \right)}}{53} + \frac{\sqrt{53} \log{\left(\sqrt{53} + 8 \right)}}{53}$$ 
-sqrt(53)*log(8 - sqrt(53))/53 - sqrt(53)*log(8 + sqrt(53) + tan(1/2))/53 + sqrt(53)*log(8 + sqrt(53))/53 + sqrt(53)*log(8 - sqrt(53) + tan(1/2))/53
Respuesta numérica [src] 
0.0727383126735392
0.0727383126735392

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

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