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Resolución de integrales/ cos^3/ xsinx/ xsinx÷cos^3x

Integral de xsinx÷cos^3x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |  x*sin(x)   
 |  -------- dx
 |     3       
 |  cos (x)    
 |             
/              
0
$$\int\limits_{0}^{1} \frac{x \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}}\, dx$$ 
Integral((x*sin(x))/cos(x)^3, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                            /x\                        3/x\                        4/x\                         2/x\       
 |                                                        2*tan|-|                   2*tan |-|                   x*tan |-|                  2*x*tan |-|       
 | x*sin(x)                      x                             \2/                         \2/                         \2/                          \2/       
 | -------- dx = C + ------------------------- - ------------------------- + ------------------------- + ------------------------- + -------------------------
 |    3                       2/x\        4/x\            2/x\        4/x\            2/x\        4/x\            2/x\        4/x\            2/x\        4/x\
 | cos (x)           2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|
 |                             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/
/
$$\int \frac{x \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}}\, dx = C + \frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                             4                                                                2                               3              
              1                           tan (1/2)                       2*tan(1/2)                     2*tan (1/2)                     2*tan (1/2)         
----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
         2             4                 2             4                 2             4                 2             4                 2             4     
2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)
$$- \frac{2 \tan{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{\tan^{4}{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{2 \tan^{3}{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{2 \tan^{2}{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{1}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2}$$ 
=
= 
                                             4                                                                2                               3              
              1                           tan (1/2)                       2*tan(1/2)                     2*tan (1/2)                     2*tan (1/2)         
----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
         2             4                 2             4                 2             4                 2             4                 2             4     
2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)   2 - 4*tan (1/2) + 2*tan (1/2)
$$- \frac{2 \tan{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{\tan^{4}{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{2 \tan^{3}{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{2 \tan^{2}{\left(\frac{1}{2} \right)}}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2} + \frac{1}{- 4 \tan^{2}{\left(\frac{1}{2} \right)} + 2 \tan^{4}{\left(\frac{1}{2} \right)} + 2}$$ 
1/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) + tan(1/2)^4/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) - 2*tan(1/2)/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) + 2*tan(1/2)^2/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4) + 2*tan(1/2)^3/(2 - 4*tan(1/2)^2 + 2*tan(1/2)^4)
Respuesta numérica [src] 
0.934055548079929
0.934055548079929

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

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