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Resolución de integrales/ cos3x/ Cos^3x/ Cos^3x*cos3x

Integral de Cos^3x*cos3x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 8/5                   
  /                    
 |                     
 |     3               
 |  cos (x)*cos(3*x) dx
 |                     
/                      
0
$$\int\limits_{0}^{\frac{8}{5}} \cos^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx$$ 
Integral(cos(x)^3*cos(3*x), (x, 0, 8/5))
Respuesta (Indefinida) [src] 
  /                                                               
 |                              3                                 
 |    3                      sin (2*x)   sin(2*x)   x   3*sin(4*x)
 | cos (x)*cos(3*x) dx = C - --------- + -------- + - + ----------
 |                               12         4       8       32    
/
$$\int \cos^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx = C + \frac{x}{8} - \frac{\sin^{3}{\left(2 x \right)}}{12} + \frac{\sin{\left(2 x \right)}}{4} + \frac{3 \sin{\left(4 x \right)}}{32}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
     3                     3                     3                       3                       2                              2                                2                        
  sin (8/5)*sin(24/5)   sin (8/5)*cos(24/5)   cos (8/5)*cos(24/5)   3*cos (8/5)*sin(24/5)   3*sin (8/5)*cos(8/5)*cos(24/5)   cos (8/5)*cos(24/5)*sin(8/5)   3*cos (8/5)*sin(8/5)*sin(24/5)
- ------------------- - ------------------- + ------------------- + --------------------- - ------------------------------ - ---------------------------- + ------------------------------
           5                     24                    5                      8                           5                               4                               5
$$- \frac{\sin^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{24} + \frac{3 \sin{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)}}{5} - \frac{\sin{\left(\frac{8}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{4} + \frac{\cos^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} + \frac{3 \sin{\left(\frac{24}{5} \right)} \cos^{3}{\left(\frac{8}{5} \right)}}{8} - \frac{3 \sin^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} - \frac{\sin^{3}{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)}}{5}$$ 
=
= 
     3                     3                     3                       3                       2                              2                                2                        
  sin (8/5)*sin(24/5)   sin (8/5)*cos(24/5)   cos (8/5)*cos(24/5)   3*cos (8/5)*sin(24/5)   3*sin (8/5)*cos(8/5)*cos(24/5)   cos (8/5)*cos(24/5)*sin(8/5)   3*cos (8/5)*sin(8/5)*sin(24/5)
- ------------------- - ------------------- + ------------------- + --------------------- - ------------------------------ - ---------------------------- + ------------------------------
           5                     24                    5                      8                           5                               4                               5
$$- \frac{\sin^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{24} + \frac{3 \sin{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)}}{5} - \frac{\sin{\left(\frac{8}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{4} + \frac{\cos^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} + \frac{3 \sin{\left(\frac{24}{5} \right)} \cos^{3}{\left(\frac{8}{5} \right)}}{8} - \frac{3 \sin^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} - \frac{\sin^{3}{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)}}{5}$$ 
-sin(8/5)^3*sin(24/5)/5 - sin(8/5)^3*cos(24/5)/24 + cos(8/5)^3*cos(24/5)/5 + 3*cos(8/5)^3*sin(24/5)/8 - 3*sin(8/5)^2*cos(8/5)*cos(24/5)/5 - cos(8/5)^2*cos(24/5)*sin(8/5)/4 + 3*cos(8/5)^2*sin(8/5)*sin(24/5)/5
Respuesta numérica [src] 
0.196349528119917
0.196349528119917

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

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