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Resolución de integrales/ cos(2x)/ (3x)^2/ cos(3x)/ cos(2x)^2*cos(3x)^2

Integral de cos(2x)^2*cos(3x)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
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 |     2         2        
 |  cos (2*x)*cos (3*x) dx
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/                         
0
$$\int\limits_{0}^{1} \cos^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)}\, dx$$ 
Integral(cos(2*x)^2*cos(3*x)^2, (x, 0, 1))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2       2         2       2         2       2         2       2         2                       2                         2                         2                 
cos (2)*cos (3)   cos (2)*sin (3)   cos (3)*sin (2)   sin (2)*sin (3)   sin (2)*cos(3)*sin(3)   cos (3)*cos(2)*sin(2)   7*cos (2)*cos(3)*sin(3)   9*sin (3)*cos(2)*sin(2)
--------------- + --------------- + --------------- + --------------- - --------------------- + --------------------- + ----------------------- + -----------------------
       4                 4                 4                 4                    15                      40                       30                        40
$$\frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos^{2}{\left(3 \right)}}{40} + \frac{7 \sin{\left(3 \right)} \cos^{2}{\left(2 \right)} \cos{\left(3 \right)}}{30} + \frac{9 \sin{\left(2 \right)} \sin^{2}{\left(3 \right)} \cos{\left(2 \right)}}{40} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \sin^{2}{\left(3 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{15} + \frac{\cos^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4}$$ 
=
= 
   2       2         2       2         2       2         2       2         2                       2                         2                         2                 
cos (2)*cos (3)   cos (2)*sin (3)   cos (3)*sin (2)   sin (2)*sin (3)   sin (2)*cos(3)*sin(3)   cos (3)*cos(2)*sin(2)   7*cos (2)*cos(3)*sin(3)   9*sin (3)*cos(2)*sin(2)
--------------- + --------------- + --------------- + --------------- - --------------------- + --------------------- + ----------------------- + -----------------------
       4                 4                 4                 4                    15                      40                       30                        40
$$\frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos^{2}{\left(3 \right)}}{40} + \frac{7 \sin{\left(3 \right)} \cos^{2}{\left(2 \right)} \cos{\left(3 \right)}}{30} + \frac{9 \sin{\left(2 \right)} \sin^{2}{\left(3 \right)} \cos{\left(2 \right)}}{40} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \sin^{2}{\left(3 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{15} + \frac{\cos^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4}$$ 
cos(2)^2*cos(3)^2/4 + cos(2)^2*sin(3)^2/4 + cos(3)^2*sin(2)^2/4 + sin(2)^2*sin(3)^2/4 - sin(2)^2*cos(3)*sin(3)/15 + cos(3)^2*cos(2)*sin(2)/40 + 7*cos(2)^2*cos(3)*sin(3)/30 + 9*sin(3)^2*cos(2)*sin(2)/40
Respuesta numérica [src] 
0.241088356908787
0.241088356908787

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

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