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Resolución de integrales/ 3sinx/ 2-3sin/ 1/(2-3sinx+cos)

Integral de 1/(2-3sinx+cos) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   0                          
   /                          
  |                           
  |             1             
  |   --------------------- dx
  |   2 - 3*sin(x) + cos(x)   
  |                           
 /                            
-157                          
-----                         
 100
∫−15710001(2−3sin⁡(x))+cos⁡(x) dx\int\limits_{- \frac{157}{100}}^{0} \frac{1}{\left(2 - 3 \sin{\left(x \right)}\right) + \cos{\left(x \right)}}\, dx 
Integral(1/(2 - 3*sin(x) + cos(x)), (x, -157/100, 0))
Respuesta (Indefinida) [src] 
  /                                 ___    /       ___      /x\\     ___    /       ___      /x\\
 |                                \/ 6 *log|-3 + \/ 6  + tan|-||   \/ 6 *log|-3 - \/ 6  + tan|-||
 |           1                             \                \2//            \                \2//
 | --------------------- dx = C - ------------------------------ + ------------------------------
 | 2 - 3*sin(x) + cos(x)                        6                                6               
 |                                                                                               
/
∫1(2−3sin⁡(x))+cos⁡(x) dx=C+6log⁡(tan⁡(x2)−3−6)6−6log⁡(tan⁡(x2)−3+6)6\int \frac{1}{\left(2 - 3 \sin{\left(x \right)}\right) + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - 3 - \sqrt{6} \right)}}{6} - \frac{\sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - 3 + \sqrt{6} \right)}}{6}
Simplificar
Gráfica
-1.5-1.4-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.01.0
Trazar el gráfico f(x)
Respuesta [src] 
                                    ___ /          /      ___      /157\\\                                     ___ /          /      ___      /157\\\
    ___ /          /      ___\\   \/ 6 *|pi*I + log|3 + \/ 6  + tan|---|||     ___ /          /      ___\\   \/ 6 *|pi*I + log|3 - \/ 6  + tan|---|||
  \/ 6 *\pi*I + log\3 - \/ 6 //         \          \               \200///   \/ 6 *\pi*I + log\3 + \/ 6 //         \          \               \200///
- ----------------------------- - ---------------------------------------- + ----------------------------- + ----------------------------------------
                6                                    6                                     6                                    6
−6(log⁡(tan⁡(157200)+6+3)+iπ)6−6(log⁡(3−6)+iπ)6+6(log⁡(−6+tan⁡(157200)+3)+iπ)6+6(log⁡(6+3)+iπ)6- \frac{\sqrt{6} \left(\log{\left(\tan{\left(\frac{157}{200} \right)} + \sqrt{6} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{6} \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(- \sqrt{6} + \tan{\left(\frac{157}{200} \right)} + 3 \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)}{6} 
=
= 
                                    ___ /          /      ___      /157\\\                                     ___ /          /      ___      /157\\\
    ___ /          /      ___\\   \/ 6 *|pi*I + log|3 + \/ 6  + tan|---|||     ___ /          /      ___\\   \/ 6 *|pi*I + log|3 - \/ 6  + tan|---|||
  \/ 6 *\pi*I + log\3 - \/ 6 //         \          \               \200///   \/ 6 *\pi*I + log\3 + \/ 6 //         \          \               \200///
- ----------------------------- - ---------------------------------------- + ----------------------------- + ----------------------------------------
                6                                    6                                     6                                    6
−6(log⁡(tan⁡(157200)+6+3)+iπ)6−6(log⁡(3−6)+iπ)6+6(log⁡(−6+tan⁡(157200)+3)+iπ)6+6(log⁡(6+3)+iπ)6- \frac{\sqrt{6} \left(\log{\left(\tan{\left(\frac{157}{200} \right)} + \sqrt{6} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{6} \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(- \sqrt{6} + \tan{\left(\frac{157}{200} \right)} + 3 \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)}{6} 
-sqrt(6)*(pi*i + log(3 - sqrt(6)))/6 - sqrt(6)*(pi*i + log(3 + sqrt(6) + tan(157/200)))/6 + sqrt(6)*(pi*i + log(3 + sqrt(6)))/6 + sqrt(6)*(pi*i + log(3 - sqrt(6) + tan(157/200)))/6
Respuesta numérica [src] 
0.353798027209071
0.353798027209071

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

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