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Resolución de integrales/ tan(x)/ sin(2x)/ (5tan(x)-2)/(2sin(2x)+5)

Integral de (5tan(x)-2)/(2sin(2x)+5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                  
 --                  
 4                   
  /                  
 |                   
 |   5*tan(x) - 2    
 |  -------------- dx
 |  2*sin(2*x) + 5   
 |                   
/                    
0
∫0π45tan⁡(x)−22sin⁡(2x)+5 dx\int\limits_{0}^{\frac{\pi}{4}} \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx 
Integral((5*tan(x) - 2)/(2*sin(2*x) + 5), (x, 0, pi/4))
Respuesta (Indefinida) [src] 
                                                             /        /    pi\                                   \
                                                             |        |x - --|       /    ____       ____       \|
  /                            /                        ____ |        |    2 |       |2*\/ 21    5*\/ 21 *tan(x)||
 |                            |                     2*\/ 21 *|pi*floor|------| + atan|-------- + ---------------||
 |  5*tan(x) - 2              |     tan(x)                   \        \  pi  /       \   21             21      //
 | -------------- dx = C + 5* | -------------- dx - --------------------------------------------------------------
 | 2*sin(2*x) + 5             | 5 + 2*sin(2*x)                                    21                              
 |                            |                                                                                   
/                            /
∫5tan⁡(x)−22sin⁡(2x)+5 dx=C−221(atan⁡(521tan⁡(x)21+22121)+π⌊x−π2π⌋)21+5∫tan⁡(x)2sin⁡(2x)+5 dx\int \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx = C - \frac{2 \sqrt{21} \left(\operatorname{atan}{\left(\frac{5 \sqrt{21} \tan{\left(x \right)}}{21} + \frac{2 \sqrt{21}}{21} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{21} + 5 \int \frac{\tan{\left(x \right)}}{2 \sin{\left(2 x \right)} + 5}\, dx
Simplificar
Respuesta [src] 
 pi                  
 --                  
 4                   
  /                  
 |                   
 |  -2 + 5*tan(x)    
 |  -------------- dx
 |  5 + 2*sin(2*x)   
 |                   
/                    
0
∫0π45tan⁡(x)−22sin⁡(2x)+5 dx\int\limits_{0}^{\frac{\pi}{4}} \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx 
=
= 
 pi                  
 --                  
 4                   
  /                  
 |                   
 |  -2 + 5*tan(x)    
 |  -------------- dx
 |  5 + 2*sin(2*x)   
 |                   
/                    
0
∫0π45tan⁡(x)−22sin⁡(2x)+5 dx\int\limits_{0}^{\frac{\pi}{4}} \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx 
Integral((-2 + 5*tan(x))/(5 + 2*sin(2*x)), (x, 0, pi/4))
Respuesta numérica [src] 
0.00885866363415532
0.00885866363415532

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

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