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Resolución de integrales/ cos(5x)/ cos(x)/ cos(2x)/ cos(x)×cos(2x)×cos(5x)

Integral de cos(x)×cos(2x)×cos(5x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
  /                            
 |                             
 |  cos(x)*cos(2*x)*cos(5*x) dx
 |                             
/                              
0
$$\int\limits_{0}^{1} \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(5 x \right)}\, dx$$ 
Integral((cos(x)*cos(2*x))*cos(5*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                     3                                      
 |                                   sin (2*x)   sin(2*x)   sin(4*x)   sin(8*x)
 | cos(x)*cos(2*x)*cos(5*x) dx = C - --------- + -------- + -------- + --------
 |                                       6          4          16         32   
/
$$\int \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(5 x \right)}\, dx = C - \frac{\sin^{3}{\left(2 x \right)}}{6} + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{16} + \frac{\sin{\left(8 x \right)}}{32}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
  11*cos(1)*cos(5)*sin(2)   7*cos(2)*cos(5)*sin(1)   5*sin(1)*sin(2)*sin(5)   25*cos(1)*cos(2)*sin(5)
- ----------------------- - ---------------------- - ---------------------- + -----------------------
             96                       96                       96                        96
$$- \frac{11 \sin{\left(2 \right)} \cos{\left(1 \right)} \cos{\left(5 \right)}}{96} - \frac{7 \sin{\left(1 \right)} \cos{\left(2 \right)} \cos{\left(5 \right)}}{96} - \frac{5 \sin{\left(1 \right)} \sin{\left(2 \right)} \sin{\left(5 \right)}}{96} + \frac{25 \sin{\left(5 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{96}$$ 
=
= 
  11*cos(1)*cos(5)*sin(2)   7*cos(2)*cos(5)*sin(1)   5*sin(1)*sin(2)*sin(5)   25*cos(1)*cos(2)*sin(5)
- ----------------------- - ---------------------- - ---------------------- + -----------------------
             96                       96                       96                        96
$$- \frac{11 \sin{\left(2 \right)} \cos{\left(1 \right)} \cos{\left(5 \right)}}{96} - \frac{7 \sin{\left(1 \right)} \cos{\left(2 \right)} \cos{\left(5 \right)}}{96} - \frac{5 \sin{\left(1 \right)} \sin{\left(2 \right)} \sin{\left(5 \right)}}{96} + \frac{25 \sin{\left(5 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{96}$$ 
-11*cos(1)*cos(5)*sin(2)/96 - 7*cos(2)*cos(5)*sin(1)/96 - 5*sin(1)*sin(2)*sin(5)/96 + 25*cos(1)*cos(2)*sin(5)/96
Respuesta numérica [src] 
0.0856371551784901
0.0856371551784901

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

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