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Resolución de integrales/ cos(x/4)/ sin(x/4)/ (sin(x/4)^2)*(cos(x/4)^6)

Integral de (sin(x/4)^2)*(cos(x/4)^6) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |     2/x\    6/x\   
 |  sin |-|*cos |-| dx
 |      \4/     \4/   
 |                    
/                     
0
∫01sin⁡2(x4)cos⁡6(x4) dx\int\limits_{0}^{1} \sin^{2}{\left(\frac{x}{4} \right)} \cos^{6}{\left(\frac{x}{4} \right)}\, dx 
Integral(sin(x/4)^2*cos(x/4)^6, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                  7/x\    /x\      5/x\    /x\        /x\    /x\        3/x\    /x\
 |                                cos |-|*sin|-|   cos |-|*sin|-|   5*cos|-|*sin|-|   5*cos |-|*sin|-|
 |    2/x\    6/x\          5*x       \4/    \4/       \4/    \4/        \4/    \4/         \4/    \4/
 | sin |-|*cos |-| dx = C + --- - -------------- + -------------- + --------------- + ----------------
 |     \4/     \4/          128         2                12                32                48       
 |                                                                                                    
/
∫sin⁡2(x4)cos⁡6(x4) dx=C+5x128−sin⁡(x4)cos⁡7(x4)2+sin⁡(x4)cos⁡5(x4)12+5sin⁡(x4)cos⁡3(x4)48+5sin⁡(x4)cos⁡(x4)32\int \sin^{2}{\left(\frac{x}{4} \right)} \cos^{6}{\left(\frac{x}{4} \right)}\, dx = C + \frac{5 x}{128} - \frac{\sin{\left(\frac{x}{4} \right)} \cos^{7}{\left(\frac{x}{4} \right)}}{2} + \frac{\sin{\left(\frac{x}{4} \right)} \cos^{5}{\left(\frac{x}{4} \right)}}{12} + \frac{5 \sin{\left(\frac{x}{4} \right)} \cos^{3}{\left(\frac{x}{4} \right)}}{48} + \frac{5 \sin{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}}{32}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.000.10
Trazar el gráfico f(x)
Respuesta [src] 
         7                    5                                            3              
 5    cos (1/4)*sin(1/4)   cos (1/4)*sin(1/4)   5*cos(1/4)*sin(1/4)   5*cos (1/4)*sin(1/4)
--- - ------------------ + ------------------ + ------------------- + --------------------
128           2                    12                    32                    48
−sin⁡(14)cos⁡7(14)2+sin⁡(14)cos⁡5(14)12+5sin⁡(14)cos⁡3(14)48+5sin⁡(14)cos⁡(14)32+5128- \frac{\sin{\left(\frac{1}{4} \right)} \cos^{7}{\left(\frac{1}{4} \right)}}{2} + \frac{\sin{\left(\frac{1}{4} \right)} \cos^{5}{\left(\frac{1}{4} \right)}}{12} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos^{3}{\left(\frac{1}{4} \right)}}{48} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{32} + \frac{5}{128} 
=
= 
         7                    5                                            3              
 5    cos (1/4)*sin(1/4)   cos (1/4)*sin(1/4)   5*cos(1/4)*sin(1/4)   5*cos (1/4)*sin(1/4)
--- - ------------------ + ------------------ + ------------------- + --------------------
128           2                    12                    32                    48
−sin⁡(14)cos⁡7(14)2+sin⁡(14)cos⁡5(14)12+5sin⁡(14)cos⁡3(14)48+5sin⁡(14)cos⁡(14)32+5128- \frac{\sin{\left(\frac{1}{4} \right)} \cos^{7}{\left(\frac{1}{4} \right)}}{2} + \frac{\sin{\left(\frac{1}{4} \right)} \cos^{5}{\left(\frac{1}{4} \right)}}{12} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos^{3}{\left(\frac{1}{4} \right)}}{48} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{32} + \frac{5}{128} 
5/128 - cos(1/4)^7*sin(1/4)/2 + cos(1/4)^5*sin(1/4)/12 + 5*cos(1/4)*sin(1/4)/32 + 5*cos(1/4)^3*sin(1/4)/48
Respuesta numérica [src] 
0.018397539259727
0.018397539259727

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

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