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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
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 |     3               
 |  cos (x)*sin(2*x) dx
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0
∫01sin⁡(2x)cos⁡3(x) dx\int\limits_{0}^{1} \sin{\left(2 x \right)} \cos^{3}{\left(x \right)}\, dx 
Integral(cos(x)^3*sin(2*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                   
 |                                5   
 |    3                      2*cos (x)
 | cos (x)*sin(2*x) dx = C - ---------
 |                               5    
/
∫sin⁡(2x)cos⁡3(x) dx=C−2cos⁡5(x)5\int \sin{\left(2 x \right)} \cos^{3}{\left(x \right)}\, dx = C - \frac{2 \cos^{5}{\left(x \right)}}{5}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901-1
Trazar el gráfico f(x)
Respuesta [src] 
         3                  3                  2                       2                 
2   2*cos (1)*cos(2)   2*sin (1)*sin(2)   4*sin (1)*cos(1)*cos(2)   cos (1)*sin(1)*sin(2)
- - ---------------- - ---------------- - ----------------------- + ---------------------
5          5                  5                      5                        5
−2sin⁡3(1)sin⁡(2)5−2cos⁡3(1)cos⁡(2)5+sin⁡(1)sin⁡(2)cos⁡2(1)5−4sin⁡2(1)cos⁡(1)cos⁡(2)5+25- \frac{2 \sin^{3}{\left(1 \right)} \sin{\left(2 \right)}}{5} - \frac{2 \cos^{3}{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{\sin{\left(1 \right)} \sin{\left(2 \right)} \cos^{2}{\left(1 \right)}}{5} - \frac{4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{2}{5} 
=
= 
         3                  3                  2                       2                 
2   2*cos (1)*cos(2)   2*sin (1)*sin(2)   4*sin (1)*cos(1)*cos(2)   cos (1)*sin(1)*sin(2)
- - ---------------- - ---------------- - ----------------------- + ---------------------
5          5                  5                      5                        5
−2sin⁡3(1)sin⁡(2)5−2cos⁡3(1)cos⁡(2)5+sin⁡(1)sin⁡(2)cos⁡2(1)5−4sin⁡2(1)cos⁡(1)cos⁡(2)5+25- \frac{2 \sin^{3}{\left(1 \right)} \sin{\left(2 \right)}}{5} - \frac{2 \cos^{3}{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{\sin{\left(1 \right)} \sin{\left(2 \right)} \cos^{2}{\left(1 \right)}}{5} - \frac{4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{2}{5} 
2/5 - 2*cos(1)^3*cos(2)/5 - 2*sin(1)^3*sin(2)/5 - 4*sin(1)^2*cos(1)*cos(2)/5 + cos(1)^2*sin(1)*sin(2)/5
Respuesta numérica [src] 
0.38158193097144
0.38158193097144

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

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