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Resolución de integrales/ 3sinx/ 1/(cosx-3sinx)

Integral de 1/(cosx-3sinx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |          1           
 |  ----------------- dx
 |  cos(x) - 3*sin(x)   
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{1}{- 3 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$ 
Integral(1/(cos(x) - 3*sin(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                             ____    /      ____      /x\\     ____    /      ____      /x\\
 |                            \/ 10 *log|3 - \/ 10  + tan|-||   \/ 10 *log|3 + \/ 10  + tan|-||
 |         1                            \                \2//             \                \2//
 | ----------------- dx = C - ------------------------------- + -------------------------------
 | cos(x) - 3*sin(x)                         10                                10              
 |                                                                                             
/
$$\int \frac{1}{- 3 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} + 3 + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{10} + 3 \right)}}{10}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ____    /      ____\     ____    /      ____           \     ____ /          /       ____\\     ____    /      ____           \
  \/ 10 *log\3 + \/ 10 /   \/ 10 *log\3 - \/ 10  + tan(1/2)/   \/ 10 *\pi*I + log\-3 + \/ 10 //   \/ 10 *log\3 + \/ 10  + tan(1/2)/
- ---------------------- - --------------------------------- + -------------------------------- + ---------------------------------
            10                             10                                 10                                  10
$$- \frac{\sqrt{10} \log{\left(3 + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \log{\left(- \sqrt{10} + \tan{\left(\frac{1}{2} \right)} + 3 \right)}}{10} + \frac{\sqrt{10} \log{\left(\tan{\left(\frac{1}{2} \right)} + 3 + \sqrt{10} \right)}}{10} + \frac{\sqrt{10} \left(\log{\left(-3 + \sqrt{10} \right)} + i \pi\right)}{10}$$ 
=
= 
    ____    /      ____\     ____    /      ____           \     ____ /          /       ____\\     ____    /      ____           \
  \/ 10 *log\3 + \/ 10 /   \/ 10 *log\3 - \/ 10  + tan(1/2)/   \/ 10 *\pi*I + log\-3 + \/ 10 //   \/ 10 *log\3 + \/ 10  + tan(1/2)/
- ---------------------- - --------------------------------- + -------------------------------- + ---------------------------------
            10                             10                                 10                                  10
$$- \frac{\sqrt{10} \log{\left(3 + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \log{\left(- \sqrt{10} + \tan{\left(\frac{1}{2} \right)} + 3 \right)}}{10} + \frac{\sqrt{10} \log{\left(\tan{\left(\frac{1}{2} \right)} + 3 + \sqrt{10} \right)}}{10} + \frac{\sqrt{10} \left(\log{\left(-3 + \sqrt{10} \right)} + i \pi\right)}{10}$$ 
-sqrt(10)*log(3 + sqrt(10))/10 - sqrt(10)*log(3 - sqrt(10) + tan(1/2))/10 + sqrt(10)*(pi*i + log(-3 + sqrt(10)))/10 + sqrt(10)*log(3 + sqrt(10) + tan(1/2))/10
Respuesta numérica [src] 
-6.16938243931863
-6.16938243931863

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

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