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Resolución de integrales/ (3*sinx+2*cosx+1)/(sinx+sin(2*x))

Integral de (3*sinx+2*cosx+1)/(sinx+sin(2*x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                           
  /                           
 |                            
 |  3*sin(x) + 2*cos(x) + 1   
 |  ----------------------- dx
 |     sin(x) + sin(2*x)      
 |                            
/                             
0
∫01(3sin⁡(x)+2cos⁡(x))+1sin⁡(x)+sin⁡(2x) dx\int\limits_{0}^{1} \frac{\left(3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx 
Integral((3*sin(x) + 2*cos(x) + 1)/(sin(x) + sin(2*x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                     /                           /                         /                    
 |                                     |                           |                         |                     
 | 3*sin(x) + 2*cos(x) + 1             |       cos(x)              |       sin(x)            |         1           
 | ----------------------- dx = C + 2* | ----------------- dx + 3* | ----------------- dx +  | ----------------- dx
 |    sin(x) + sin(2*x)                | sin(x) + sin(2*x)         | sin(x) + sin(2*x)       | sin(x) + sin(2*x)   
 |                                     |                           |                         |                     
/                                     /                           /                         /
∫(3sin⁡(x)+2cos⁡(x))+1sin⁡(x)+sin⁡(2x) dx=C+3∫sin⁡(x)sin⁡(x)+sin⁡(2x) dx+2∫cos⁡(x)sin⁡(x)+sin⁡(2x) dx+∫1sin⁡(x)+sin⁡(2x) dx\int \frac{\left(3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx = C + 3 \int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx + 2 \int \frac{\cos{\left(x \right)}}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx + \int \frac{1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx
Simplificar
Respuesta [src] 
  1                           
  /                           
 |                            
 |  1 + 2*cos(x) + 3*sin(x)   
 |  ----------------------- dx
 |     sin(x) + sin(2*x)      
 |                            
/                             
0
∫013sin⁡(x)+2cos⁡(x)+1sin⁡(x)+sin⁡(2x) dx\int\limits_{0}^{1} \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx 
=
= 
  1                           
  /                           
 |                            
 |  1 + 2*cos(x) + 3*sin(x)   
 |  ----------------------- dx
 |     sin(x) + sin(2*x)      
 |                            
/                             
0
∫013sin⁡(x)+2cos⁡(x)+1sin⁡(x)+sin⁡(2x) dx\int\limits_{0}^{1} \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx 
Integral((1 + 2*cos(x) + 3*sin(x))/(sin(x) + sin(2*x)), (x, 0, 1))
Respuesta numérica [src] 
45.3101766649577
45.3101766649577

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

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