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Resolución de integrales/ cos^2/ cos^2(p/6-x)dx

Integral de cos^2(p/6-x)dx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  p               
  -               
  2               
  /               
 |                
 |     2/p    \   
 |  cos |- - x| dx
 |      \6    /   
 |                
/                 
E
∫ep2cos⁡2(p6−x) dx\int\limits_{e}^{\frac{p}{2}} \cos^{2}{\left(\frac{p}{6} - x \right)}\, dx 
Integral(cos(p/6 - x)^2, (x, E, p/2))
Respuesta (Indefinida) [src] 
  /                                                                                /  x   p \                                3/  x   p \                               4/  x   p \                                2/  x   p \          
 |                                                                            2*tan|- - + --|                           2*tan |- - + --|                          x*tan |- - + --|                         2*x*tan |- - + --|          
 |    2/p    \                             x                                       \  2   12/                                 \  2   12/                                \  2   12/                                 \  2   12/          
 | cos |- - x| dx = C + --------------------------------------- - --------------------------------------- + --------------------------------------- + --------------------------------------- + ---------------------------------------
 |     \6    /                   4/  x   p \        2/  x   p \            4/  x   p \        2/  x   p \            4/  x   p \        2/  x   p \            4/  x   p \        2/  x   p \            4/  x   p \        2/  x   p \
 |                      2 + 2*tan |- - + --| + 4*tan |- - + --|   2 + 2*tan |- - + --| + 4*tan |- - + --|   2 + 2*tan |- - + --| + 4*tan |- - + --|   2 + 2*tan |- - + --| + 4*tan |- - + --|   2 + 2*tan |- - + --| + 4*tan |- - + --|
/                                 \  2   12/         \  2   12/             \  2   12/         \  2   12/             \  2   12/         \  2   12/             \  2   12/         \  2   12/             \  2   12/         \  2   12/
∫cos⁡2(p6−x) dx=C+xtan⁡4(p12−x2)2tan⁡4(p12−x2)+4tan⁡2(p12−x2)+2+2xtan⁡2(p12−x2)2tan⁡4(p12−x2)+4tan⁡2(p12−x2)+2+x2tan⁡4(p12−x2)+4tan⁡2(p12−x2)+2+2tan⁡3(p12−x2)2tan⁡4(p12−x2)+4tan⁡2(p12−x2)+2−2tan⁡(p12−x2)2tan⁡4(p12−x2)+4tan⁡2(p12−x2)+2\int \cos^{2}{\left(\frac{p}{6} - x \right)}\, dx = C + \frac{x \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} + \frac{2 \tan^{3}{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} - \frac{2 \tan{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2}
Simplificar
Respuesta [src] 
   /p\    /p\      /     p\    /     p\        2/     p\        2/     p\        2/p\        2/p\
cos|-|*sin|-|   cos|-E + -|*sin|-E + -|   E*cos |-E + -|   E*sin |-E + -|   p*cos |-|   p*sin |-|
   \3/    \3/      \     6/    \     6/         \     6/         \     6/         \3/         \3/
------------- + ----------------------- - -------------- - -------------- + --------- + ---------
      2                    2                    2                2              4           4
psin⁡2(p3)4+pcos⁡2(p3)4+sin⁡(p3)cos⁡(p3)2−esin⁡2(p6−e)2+sin⁡(p6−e)cos⁡(p6−e)2−ecos⁡2(p6−e)2\frac{p \sin^{2}{\left(\frac{p}{3} \right)}}{4} + \frac{p \cos^{2}{\left(\frac{p}{3} \right)}}{4} + \frac{\sin{\left(\frac{p}{3} \right)} \cos{\left(\frac{p}{3} \right)}}{2} - \frac{e \sin^{2}{\left(\frac{p}{6} - e \right)}}{2} + \frac{\sin{\left(\frac{p}{6} - e \right)} \cos{\left(\frac{p}{6} - e \right)}}{2} - \frac{e \cos^{2}{\left(\frac{p}{6} - e \right)}}{2} 
=
= 
   /p\    /p\      /     p\    /     p\        2/     p\        2/     p\        2/p\        2/p\
cos|-|*sin|-|   cos|-E + -|*sin|-E + -|   E*cos |-E + -|   E*sin |-E + -|   p*cos |-|   p*sin |-|
   \3/    \3/      \     6/    \     6/         \     6/         \     6/         \3/         \3/
------------- + ----------------------- - -------------- - -------------- + --------- + ---------
      2                    2                    2                2              4           4
psin⁡2(p3)4+pcos⁡2(p3)4+sin⁡(p3)cos⁡(p3)2−esin⁡2(p6−e)2+sin⁡(p6−e)cos⁡(p6−e)2−ecos⁡2(p6−e)2\frac{p \sin^{2}{\left(\frac{p}{3} \right)}}{4} + \frac{p \cos^{2}{\left(\frac{p}{3} \right)}}{4} + \frac{\sin{\left(\frac{p}{3} \right)} \cos{\left(\frac{p}{3} \right)}}{2} - \frac{e \sin^{2}{\left(\frac{p}{6} - e \right)}}{2} + \frac{\sin{\left(\frac{p}{6} - e \right)} \cos{\left(\frac{p}{6} - e \right)}}{2} - \frac{e \cos^{2}{\left(\frac{p}{6} - e \right)}}{2} 
cos(p/3)*sin(p/3)/2 + cos(-E + p/6)*sin(-E + p/6)/2 - E*cos(-E + p/6)^2/2 - E*sin(-E + p/6)^2/2 + p*cos(p/3)^2/4 + p*sin(p/3)^2/4

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

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