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Resolución de integrales/ (1+cos(4x))/2*(1+2cos(2x)+cos^2(2x))

Integral de (1+cos(4x))/2*(1+2cos(2x)+cos^2(2x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                                             
  /                                             
 |                                              
 |  1 + cos(4*x) /                    2     \   
 |  ------------*\1 + 2*cos(2*x) + cos (2*x)/ dx
 |       2                                      
 |                                              
/                                               
0
∫01cos⁡(4x)+12((2cos⁡(2x)+1)+cos⁡2(2x)) dx\int\limits_{0}^{1} \frac{\cos{\left(4 x \right)} + 1}{2} \left(\left(2 \cos{\left(2 x \right)} + 1\right) + \cos^{2}{\left(2 x \right)}\right)\, dx 
Integral(((1 + cos(4*x))/2)*(1 + 2*cos(2*x) + cos(2*x)^2), (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9005
Trazar el gráfico f(x)
Respuesta [src] 
                2         2                                  2                                2                2                                                                        
1   sin(2)   cos (2)   sin (2)   sin(4)   cos(4)*sin(2)   sin (2)*cos(4)   cos(2)*sin(4)   cos (2)*cos(4)   cos (2)*sin(4)   cos(2)*sin(2)   cos(2)*cos(4)*sin(2)   cos(2)*sin(2)*sin(4)
- + ------ + ------- + ------- + ------ - ------------- - -------------- + ------------- + -------------- + -------------- + ------------- - -------------------- + --------------------
2     2         4         4        8            6               8                3               8                8                8                  16                     4
sin⁡(4)8+sin⁡(2)cos⁡(2)8+sin⁡(4)cos⁡2(2)8−sin⁡(2)cos⁡(2)cos⁡(4)16+cos⁡2(2)cos⁡(4)8+cos⁡2(2)4−sin⁡2(2)cos⁡(4)8+sin⁡(2)sin⁡(4)cos⁡(2)4−sin⁡(2)cos⁡(4)6+sin⁡(4)cos⁡(2)3+sin⁡2(2)4+sin⁡(2)2+12\frac{\sin{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{8} + \frac{\sin{\left(4 \right)} \cos^{2}{\left(2 \right)}}{8} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos{\left(4 \right)}}{16} + \frac{\cos^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\cos^{2}{\left(2 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \sin{\left(4 \right)} \cos{\left(2 \right)}}{4} - \frac{\sin{\left(2 \right)} \cos{\left(4 \right)}}{6} + \frac{\sin{\left(4 \right)} \cos{\left(2 \right)}}{3} + \frac{\sin^{2}{\left(2 \right)}}{4} + \frac{\sin{\left(2 \right)}}{2} + \frac{1}{2} 
=
= 
                2         2                                  2                                2                2                                                                        
1   sin(2)   cos (2)   sin (2)   sin(4)   cos(4)*sin(2)   sin (2)*cos(4)   cos(2)*sin(4)   cos (2)*cos(4)   cos (2)*sin(4)   cos(2)*sin(2)   cos(2)*cos(4)*sin(2)   cos(2)*sin(2)*sin(4)
- + ------ + ------- + ------- + ------ - ------------- - -------------- + ------------- + -------------- + -------------- + ------------- - -------------------- + --------------------
2     2         4         4        8            6               8                3               8                8                8                  16                     4
sin⁡(4)8+sin⁡(2)cos⁡(2)8+sin⁡(4)cos⁡2(2)8−sin⁡(2)cos⁡(2)cos⁡(4)16+cos⁡2(2)cos⁡(4)8+cos⁡2(2)4−sin⁡2(2)cos⁡(4)8+sin⁡(2)sin⁡(4)cos⁡(2)4−sin⁡(2)cos⁡(4)6+sin⁡(4)cos⁡(2)3+sin⁡2(2)4+sin⁡(2)2+12\frac{\sin{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{8} + \frac{\sin{\left(4 \right)} \cos^{2}{\left(2 \right)}}{8} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos{\left(4 \right)}}{16} + \frac{\cos^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\cos^{2}{\left(2 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \sin{\left(4 \right)} \cos{\left(2 \right)}}{4} - \frac{\sin{\left(2 \right)} \cos{\left(4 \right)}}{6} + \frac{\sin{\left(4 \right)} \cos{\left(2 \right)}}{3} + \frac{\sin^{2}{\left(2 \right)}}{4} + \frac{\sin{\left(2 \right)}}{2} + \frac{1}{2} 
1/2 + sin(2)/2 + cos(2)^2/4 + sin(2)^2/4 + sin(4)/8 - cos(4)*sin(2)/6 - sin(2)^2*cos(4)/8 + cos(2)*sin(4)/3 + cos(2)^2*cos(4)/8 + cos(2)^2*sin(4)/8 + cos(2)*sin(2)/8 - cos(2)*cos(4)*sin(2)/16 + cos(2)*sin(2)*sin(4)/4
Respuesta numérica [src] 
1.35994654404586
1.35994654404586

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

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