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Resolución de integrales/ cos(3x)/ sin(x)/ cos(3x)sin(x)^3

Integral de cos(3x)sin(x)^3 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
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 |  cos(3*x)*sin (x) dx
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0
$$\int\limits_{0}^{1} \sin^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx$$ 
Integral(cos(3*x)*sin(x)^3, (x, 0, 1))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
          3                3                3                  3                  2                         2                       2                 
  1    cos (1)*sin(3)   sin (1)*cos(3)   cos (1)*cos(3)   3*sin (1)*sin(3)   3*cos (1)*cos(3)*sin(1)   3*sin (1)*cos(1)*sin(3)   sin (1)*cos(1)*cos(3)
- -- + -------------- + -------------- + -------------- + ---------------- - ----------------------- - ----------------------- + ---------------------
  24         8                8                24                8                      8                         8                        4
$$\frac{\sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{4} + \frac{\sin^{3}{\left(1 \right)} \cos{\left(3 \right)}}{8} - \frac{1}{24} - \frac{3 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{8} + \frac{\cos^{3}{\left(1 \right)} \cos{\left(3 \right)}}{24} + \frac{\sin{\left(3 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{3}{\left(1 \right)} \sin{\left(3 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{8}$$ 
=
= 
          3                3                3                  3                  2                         2                       2                 
  1    cos (1)*sin(3)   sin (1)*cos(3)   cos (1)*cos(3)   3*sin (1)*sin(3)   3*cos (1)*cos(3)*sin(1)   3*sin (1)*cos(1)*sin(3)   sin (1)*cos(1)*cos(3)
- -- + -------------- + -------------- + -------------- + ---------------- - ----------------------- - ----------------------- + ---------------------
  24         8                8                24                8                      8                         8                        4
$$\frac{\sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{4} + \frac{\sin^{3}{\left(1 \right)} \cos{\left(3 \right)}}{8} - \frac{1}{24} - \frac{3 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{8} + \frac{\cos^{3}{\left(1 \right)} \cos{\left(3 \right)}}{24} + \frac{\sin{\left(3 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{3}{\left(1 \right)} \sin{\left(3 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{8}$$ 
-1/24 + cos(1)^3*sin(3)/8 + sin(1)^3*cos(3)/8 + cos(1)^3*cos(3)/24 + 3*sin(1)^3*sin(3)/8 - 3*cos(1)^2*cos(3)*sin(1)/8 - 3*sin(1)^2*cos(1)*sin(3)/8 + sin(1)^2*cos(1)*cos(3)/4
Respuesta numérica [src] 
-0.11132822809141
-0.11132822809141

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

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