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Resolución de integrales/ 8sinx/ 6cosx/ 1/(7+8sinx+6cosx)

Integral de 1/(7+8sinx+6cosx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                           
  /                           
 |                            
 |             1              
 |  ----------------------- dx
 |  7 + 8*sin(x) + 6*cos(x)   
 |                            
/                             
0
$$\int\limits_{0}^{1} \frac{1}{\left(8 \sin{\left(x \right)} + 7\right) + 6 \cos{\left(x \right)}}\, dx$$ 
Integral(1/(7 + 8*sin(x) + 6*cos(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                   ____    /      ____      /x\\     ____    /      ____      /x\\
 |                                  \/ 51 *log|8 + \/ 51  + tan|-||   \/ 51 *log|8 - \/ 51  + tan|-||
 |            1                               \                \2//             \                \2//
 | ----------------------- dx = C - ------------------------------- + -------------------------------
 | 7 + 8*sin(x) + 6*cos(x)                         51                                51              
 |                                                                                                   
/
$$\int \frac{1}{\left(8 \sin{\left(x \right)} + 7\right) + 6 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{51} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{51} + 8 \right)}}{51} - \frac{\sqrt{51} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{51} + 8 \right)}}{51}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ____    /      ____\     ____    /      ____           \     ____    /      ____\     ____    /      ____           \
  \/ 51 *log\8 - \/ 51 /   \/ 51 *log\8 + \/ 51  + tan(1/2)/   \/ 51 *log\8 + \/ 51 /   \/ 51 *log\8 - \/ 51  + tan(1/2)/
- ---------------------- - --------------------------------- + ---------------------- + ---------------------------------
            51                             51                            51                             51
$$- \frac{\sqrt{51} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{51} + 8 \right)}}{51} - \frac{\sqrt{51} \log{\left(8 - \sqrt{51} \right)}}{51} + \frac{\sqrt{51} \log{\left(- \sqrt{51} + \tan{\left(\frac{1}{2} \right)} + 8 \right)}}{51} + \frac{\sqrt{51} \log{\left(\sqrt{51} + 8 \right)}}{51}$$ 
=
= 
    ____    /      ____\     ____    /      ____           \     ____    /      ____\     ____    /      ____           \
  \/ 51 *log\8 - \/ 51 /   \/ 51 *log\8 + \/ 51  + tan(1/2)/   \/ 51 *log\8 + \/ 51 /   \/ 51 *log\8 - \/ 51  + tan(1/2)/
- ---------------------- - --------------------------------- + ---------------------- + ---------------------------------
            51                             51                            51                             51
$$- \frac{\sqrt{51} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{51} + 8 \right)}}{51} - \frac{\sqrt{51} \log{\left(8 - \sqrt{51} \right)}}{51} + \frac{\sqrt{51} \log{\left(- \sqrt{51} + \tan{\left(\frac{1}{2} \right)} + 8 \right)}}{51} + \frac{\sqrt{51} \log{\left(\sqrt{51} + 8 \right)}}{51}$$ 
-sqrt(51)*log(8 - sqrt(51))/51 - sqrt(51)*log(8 + sqrt(51) + tan(1/2))/51 + sqrt(51)*log(8 + sqrt(51))/51 + sqrt(51)*log(8 - sqrt(51) + tan(1/2))/51
Respuesta numérica [src] 
0.0639911967483684
0.0639911967483684

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

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