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Resolución de integrales/ tgx-1/ sin2x/ (3*tgx-10)/((tgx-5)*sin2x)

Integral de (3*tgx-10)/((tgx-5)*sin2x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 atan(2)                        
    /                           
   |                            
   |        3*tan(x) - 10       
   |    --------------------- dx
   |    (tan(x) - 5)*sin(2*x)   
   |                            
  /                             
  pi                            
  --                            
  4
∫π4atan⁡(2)3tan⁡(x)−10(tan⁡(x)−5)sin⁡(2x) dx\int\limits_{\frac{\pi}{4}}^{\operatorname{atan}{\left(2 \right)}} \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx 
Integral((3*tan(x) - 10)/(((tan(x) - 5)*sin(2*x))), (x, pi/4, atan(2)))
Respuesta (Indefinida) [src] 
  /                                    /                                /                         
 |                                    |                                |                          
 |     3*tan(x) - 10                  |           1                    |         tan(x)           
 | --------------------- dx = C - 10* | ---------------------- dx + 3* | ---------------------- dx
 | (tan(x) - 5)*sin(2*x)              | (-5 + tan(x))*sin(2*x)         | (-5 + tan(x))*sin(2*x)   
 |                                    |                                |                          
/                                    /                                /
∫3tan⁡(x)−10(tan⁡(x)−5)sin⁡(2x) dx=C−10∫1(tan⁡(x)−5)sin⁡(2x) dx+3∫tan⁡(x)(tan⁡(x)−5)sin⁡(2x) dx\int \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx = C - 10 \int \frac{1}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx + 3 \int \frac{\tan{\left(x \right)}}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx
Simplificar
Respuesta [src] 
 atan(2)                         
    /                            
   |                             
   |        -10 + 3*tan(x)       
   |    ---------------------- dx
   |    (-5 + tan(x))*sin(2*x)   
   |                             
  /                              
  pi                             
  --                             
  4
∫π4atan⁡(2)3tan⁡(x)−10(tan⁡(x)−5)sin⁡(2x) dx\int\limits_{\frac{\pi}{4}}^{\operatorname{atan}{\left(2 \right)}} \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx 
=
= 
 atan(2)                         
    /                            
   |                             
   |        -10 + 3*tan(x)       
   |    ---------------------- dx
   |    (-5 + tan(x))*sin(2*x)   
   |                             
  /                              
  pi                             
  --                             
  4
∫π4atan⁡(2)3tan⁡(x)−10(tan⁡(x)−5)sin⁡(2x) dx\int\limits_{\frac{\pi}{4}}^{\operatorname{atan}{\left(2 \right)}} \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx 
Integral((-10 + 3*tan(x))/((-5 + tan(x))*sin(2*x)), (x, pi/4, atan(2)))
Respuesta numérica [src] 
0.549306144334055
0.549306144334055

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

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