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  • Integral de d{x}:
  • Integral de (x+1)/(x(x-2))
  • Integral de x^1-x*dx
  • Integral de ((x^2+1)^(1/2))/x
  • Integral de (x+1)/x(x^2+1)

  • Expresiones idénticas

  • (cos(dos x))^ dos *(sin(x/ dos))^2
  • ( coseno de (2x)) al cuadrado multiplicar por ( seno de (x dividir por 2)) al cuadrado
  • ( coseno de (dos x)) en el grado dos multiplicar por ( seno de (x dividir por dos)) al cuadrado
  • (cos(2x))2*(sin(x/2))2
  • cos2x2*sinx/22
  • (cos(2x))²*(sin(x/2))²
  • (cos(2x)) en el grado 2*(sin(x/2)) en el grado 2
  • (cos(2x))^2(sin(x/2))^2
  • (cos(2x))2(sin(x/2))2
  • cos2x2sinx/22
  • cos2x^2sinx/2^2
  • (cos(2x))^2*(sin(x dividir por 2))^2
  • (cos(2x))^2*(sin(x/2))^2dx
Resolución de integrales/ cos(2x)/ sin(x/2)/ (cos(2x))^2*(sin(x/2))^2

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |     2         2/x\   
 |  cos (2*x)*sin |-| dx
 |                \2/   
 |                      
/                       
0
$$\int\limits_{0}^{1} \sin^{2}{\left(\frac{x}{2} \right)} \cos^{2}{\left(2 x \right)}\, dx$$ 
Integral(cos(2*x)^2*sin(x/2)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                        
 |                                 5                                   3   
 |    2         2/x\          2*sin (x)   sin(x)   x   sin(4*x)   2*sin (x)
 | cos (2*x)*sin |-| dx = C - --------- - ------ + - + -------- + ---------
 |               \2/              5         2      4      16          3    
 |                                                                         
/
$$\int \sin^{2}{\left(\frac{x}{2} \right)} \cos^{2}{\left(2 x \right)}\, dx = C + \frac{x}{4} - \frac{2 \sin^{5}{\left(x \right)}}{5} + \frac{2 \sin^{3}{\left(x \right)}}{3} - \frac{\sin{\left(x \right)}}{2} + \frac{\sin{\left(4 x \right)}}{16}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2         2         2         2       2           2         2           2                             2                           2                            2                   
cos (1/2)*cos (2)   cos (1/2)*sin (2)   cos (2)*sin (1/2)   sin (1/2)*sin (2)   8*sin (2)*cos(1/2)*sin(1/2)   7*cos (2)*cos(1/2)*sin(1/2)   cos (1/2)*cos(2)*sin(2)   31*sin (1/2)*cos(2)*sin(2)
----------------- + ----------------- + ----------------- + ----------------- - --------------------------- - --------------------------- - ----------------------- + --------------------------
        4                   4                   4                   4                        15                            15                         120                        120
$$- \frac{8 \sin{\left(\frac{1}{2} \right)} \sin^{2}{\left(2 \right)} \cos{\left(\frac{1}{2} \right)}}{15} - \frac{7 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)} \cos^{2}{\left(2 \right)}}{15} + \frac{31 \sin^{2}{\left(\frac{1}{2} \right)} \sin{\left(2 \right)} \cos{\left(2 \right)}}{120} - \frac{\sin{\left(2 \right)} \cos^{2}{\left(\frac{1}{2} \right)} \cos{\left(2 \right)}}{120} + \frac{\sin^{2}{\left(\frac{1}{2} \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\cos^{2}{\left(\frac{1}{2} \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(\frac{1}{2} \right)} \sin^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(\frac{1}{2} \right)}}{4}$$ 
=
= 
   2         2         2         2         2       2           2         2           2                             2                           2                            2                   
cos (1/2)*cos (2)   cos (1/2)*sin (2)   cos (2)*sin (1/2)   sin (1/2)*sin (2)   8*sin (2)*cos(1/2)*sin(1/2)   7*cos (2)*cos(1/2)*sin(1/2)   cos (1/2)*cos(2)*sin(2)   31*sin (1/2)*cos(2)*sin(2)
----------------- + ----------------- + ----------------- + ----------------- - --------------------------- - --------------------------- - ----------------------- + --------------------------
        4                   4                   4                   4                        15                            15                         120                        120
$$- \frac{8 \sin{\left(\frac{1}{2} \right)} \sin^{2}{\left(2 \right)} \cos{\left(\frac{1}{2} \right)}}{15} - \frac{7 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)} \cos^{2}{\left(2 \right)}}{15} + \frac{31 \sin^{2}{\left(\frac{1}{2} \right)} \sin{\left(2 \right)} \cos{\left(2 \right)}}{120} - \frac{\sin{\left(2 \right)} \cos^{2}{\left(\frac{1}{2} \right)} \cos{\left(2 \right)}}{120} + \frac{\sin^{2}{\left(\frac{1}{2} \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\cos^{2}{\left(\frac{1}{2} \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(\frac{1}{2} \right)} \sin^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(\frac{1}{2} \right)}}{4}$$ 
cos(1/2)^2*cos(2)^2/4 + cos(1/2)^2*sin(2)^2/4 + cos(2)^2*sin(1/2)^2/4 + sin(1/2)^2*sin(2)^2/4 - 8*sin(2)^2*cos(1/2)*sin(1/2)/15 - 7*cos(2)^2*cos(1/2)*sin(1/2)/15 - cos(1/2)^2*cos(2)*sin(2)/120 + 31*sin(1/2)^2*cos(2)*sin(2)/120
Respuesta numérica [src] 
0.010425204372031
0.010425204372031

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

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