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Resolución de integrales/ (2*cos(x)+3*sin(x))/(2sin(x)-3*cos(x))^3

Integral de (2*cos(x)+3*sin(x))/(2sin(x)-3*cos(x))^3 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                          
 --                          
 4                           
  /                          
 |                           
 |   2*cos(x) + 3*sin(x)     
 |  ---------------------- dx
 |                       3   
 |  (2*sin(x) - 3*cos(x))    
 |                           
/                            
0
∫0π43sin⁡(x)+2cos⁡(x)(2sin⁡(x)−3cos⁡(x))3 dx\int\limits_{0}^{\frac{\pi}{4}} \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)^{3}}\, dx 
Integral((2*cos(x) + 3*sin(x))/(2*sin(x) - 3*cos(x))^3, (x, 0, pi/4))
Respuesta (Indefinida) [src] 
  /                                                             /x\                                                    2/x\                                                     2/x\                                                       3/x\                      
 |                                                        12*tan|-|                                               6*tan |-|                                                8*tan |-|                                                 12*tan |-|                      
 |  2*cos(x) + 3*sin(x)                                         \2/                                                     \2/                                                      \2/                                                        \2/                      
 | ---------------------- dx = C - ------------------------------------------------------- - ---------------------------------------------------- + ------------------------------------------------------- + -------------------------------------------------------
 |                      3                      /x\         2/x\         4/x\          3/x\              /x\        2/x\         4/x\         3/x\               /x\         2/x\         4/x\          3/x\               /x\         2/x\         4/x\          3/x\
 | (2*sin(x) - 3*cos(x))           81 - 216*tan|-| - 18*tan |-| + 81*tan |-| + 216*tan |-|   27 - 72*tan|-| - 6*tan |-| + 27*tan |-| + 72*tan |-|   81 - 216*tan|-| - 18*tan |-| + 81*tan |-| + 216*tan |-|   81 - 216*tan|-| - 18*tan |-| + 81*tan |-| + 216*tan |-|
 |                                             \2/          \2/          \2/           \2/              \2/         \2/          \2/          \2/               \2/          \2/          \2/           \2/               \2/          \2/          \2/           \2/
/
∫3sin⁡(x)+2cos⁡(x)(2sin⁡(x)−3cos⁡(x))3 dx=C+12tan⁡3(x2)81tan⁡4(x2)+216tan⁡3(x2)−18tan⁡2(x2)−216tan⁡(x2)+81+8tan⁡2(x2)81tan⁡4(x2)+216tan⁡3(x2)−18tan⁡2(x2)−216tan⁡(x2)+81−12tan⁡(x2)81tan⁡4(x2)+216tan⁡3(x2)−18tan⁡2(x2)−216tan⁡(x2)+81−6tan⁡2(x2)27tan⁡4(x2)+72tan⁡3(x2)−6tan⁡2(x2)−72tan⁡(x2)+27\int \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)^{3}}\, dx = C + \frac{12 \tan^{3}{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} + 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} - 216 \tan{\left(\frac{x}{2} \right)} + 81} + \frac{8 \tan^{2}{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} + 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} - 216 \tan{\left(\frac{x}{2} \right)} + 81} - \frac{12 \tan{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} + 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} - 216 \tan{\left(\frac{x}{2} \right)} + 81} - \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{27 \tan^{4}{\left(\frac{x}{2} \right)} + 72 \tan^{3}{\left(\frac{x}{2} \right)} - 6 \tan^{2}{\left(\frac{x}{2} \right)} - 72 \tan{\left(\frac{x}{2} \right)} + 27}
Simplificar
Gráfica
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75-2010
Trazar el gráfico f(x)
Respuesta [src] 
-17 
----
 18
−1718- \frac{17}{18} 
=
= 
-17 
----
 18
−1718- \frac{17}{18} 
-17/18
Respuesta numérica [src] 
-0.944444444444444
-0.944444444444444

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

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