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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |   5*tan(x) + 2    
 |  -------------- dx
 |  2*sin(2*x) + 5   
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{5 \tan{\left(x \right)} + 2}{2 \sin{\left(2 x \right)} + 5}\, dx$$ 
Integral((5*tan(x) + 2)/(2*sin(2*x) + 5), (x, 0, 1))
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                              
 |                            |                                                                                   
/                            /
$$\int \frac{5 \tan{\left(x \right)} + 2}{2 \sin{\left(2 x \right)} + 5}\, dx = C + \frac{2 \sqrt{21} \left(\operatorname{atan}{\left(\frac{5 \sqrt{21} \tan{\left(x \right)}}{21} + \frac{2 \sqrt{21}}{21} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{21} + 5 \int \frac{\tan{\left(x \right)}}{2 \sin{\left(2 x \right)} + 5}\, dx$$
Simplificar
Respuesta [src] 
  1                  
  /                  
 |                   
 |   2 + 5*tan(x)    
 |  -------------- dx
 |  5 + 2*sin(2*x)   
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{5 \tan{\left(x \right)} + 2}{2 \sin{\left(2 x \right)} + 5}\, dx$$ 
=
= 
  1                  
  /                  
 |                   
 |   2 + 5*tan(x)    
 |  -------------- dx
 |  5 + 2*sin(2*x)   
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{5 \tan{\left(x \right)} + 2}{2 \sin{\left(2 x \right)} + 5}\, dx$$ 
Integral((2 + 5*tan(x))/(5 + 2*sin(2*x)), (x, 0, 1))
Respuesta numérica [src] 
0.770734222888298
0.770734222888298

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

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