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Expresiones idénticas
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2sin2x/cos2x-1
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2*sin^2(x)/cos^2(x-1)dx
Expresiones semejantes
2*sin^2(x)/cos^2(x+1)
Expresiones con funciones
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Coseno cos
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Resolución de integrales/ cos^2/ sin^2/ (x-1)/ 2*sin^2(x)/cos^2(x-1)

Integral de 2*sin^2(x)/cos^2(x-1) dx

Solución

Ha introducido [src]

  6               
  /               
 |                
 |        2       
 |   2*sin (x)    
 |  ----------- dx
 |     2          
 |  cos (x - 1)   
 |                
/                 
-5

\int\limits_{-5}^{6} \frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x - 1 \right)}}\, dx

Integral((2*sin(x)^2)/cos(x - 1)^2, (x, -5, 6))

Respuesta (Indefinida) [src]

  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
 |       2                                                                                  4                                                                                                                                           2       2                                                                                                                                            4                                                                                                                        2       2                                                                                                                                        3                                                                                                                                                                 2       2                                                                                                                                       3                                                                                                                                               3                                                                           
 |  2*sin (x)                                                                          2*cos (1)*cos(x)                                                                                                                            2*cos (1)*sin (1)*cos(x)                                                                                                                           2*x*sin (1)*sin(x)                                                                                                         4*cos (1)*sin (1)*cos(x)*log(cos(1)*cos(x) + sin(1)*sin(x))                                                                                      4*sin (1)*cos(1)*log(cos(1)*cos(x) + sin(1)*sin(x))*sin(x)                                                                                                      2*x*cos (1)*sin (1)*sin(x)                                                                                                                      2*x*cos (1)*cos(x)*sin(1)                                                                                                                       2*x*sin (1)*cos(1)*cos(x)                                                          
 | ----------- dx = C - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------
 |    2                    6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3                6                4       2                5                       5                         2       4                  3       3          
 | cos (x - 1)          sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)   sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x)
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
/

\int \frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x - 1 \right)}}\, dx = C - \frac{2 x \sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} + \frac{2 x \sin^{4}{\left(1 \right)} \sin{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{2 x \sin{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} + \frac{2 x \sin^{3}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{4 \log{\left(\sin{\left(1 \right)} \sin{\left(x \right)} + \cos{\left(1 \right)} \cos{\left(x \right)} \right)} \sin^{3}{\left(1 \right)} \sin{\left(x \right)} \cos{\left(1 \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{4 \log{\left(\sin{\left(1 \right)} \sin{\left(x \right)} + \cos{\left(1 \right)} \cos{\left(x \right)} \right)} \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{2 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{2 \cos^{4}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}}

Simplificar

Respuesta numérica [src]

247811.939792071

247811.939792071

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

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Integral de 2*sin^2(x)/cos^2(x-1) dx

Límites de integración:

Gráfico:

Definida a trozos:

Solución