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Resolución de integrales/ tan(x)/ xacos(tan(x)(x))

Integral de xacos(tan(x)(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
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 |  x*acos(tan(x)*x) dx
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0
∫01xacos⁡(xtan⁡(x)) dx\int\limits_{0}^{1} x \operatorname{acos}{\left(x \tan{\left(x \right)} \right)}\, dx 
Integral(x*acos(tan(x)*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               /                                           /                                           /                                                          
                              |                                           |                                           |                                                           
                              |                   3                       |               2                           |               3    2                                      
                              |                  x                        |              x *tan(x)                    |              x *tan (x)                                   
                              | ----------------------------------- dx    | ----------------------------------- dx    | ----------------------------------- dx                    
                              |   _________________________________       |   _________________________________       |   _________________________________                       
                              | \/ -(1 + x*tan(x))*(-1 + x*tan(x))        | \/ -(1 + x*tan(x))*(-1 + x*tan(x))        | \/ -(1 + x*tan(x))*(-1 + x*tan(x))                        
  /                           |                                           |                                           |                                           2               
 |                           /                                           /                                           /                                           x *acos(tan(x)*x)
 | x*acos(tan(x)*x) dx = C + ----------------------------------------- + ----------------------------------------- + ----------------------------------------- + -----------------
 |                                               2                                           2                                           2                               2        
/
∫xacos⁡(xtan⁡(x)) dx=C+x2acos⁡(xtan⁡(x))2+∫x3−(xtan⁡(x)−1)(xtan⁡(x)+1) dx2+∫x2tan⁡(x)−(xtan⁡(x)−1)(xtan⁡(x)+1) dx2+∫x3tan⁡2(x)−(xtan⁡(x)−1)(xtan⁡(x)+1) dx2\int x \operatorname{acos}{\left(x \tan{\left(x \right)} \right)}\, dx = C + \frac{x^{2} \operatorname{acos}{\left(x \tan{\left(x \right)} \right)}}{2} + \frac{\int \frac{x^{3}}{\sqrt{- \left(x \tan{\left(x \right)} - 1\right) \left(x \tan{\left(x \right)} + 1\right)}}\, dx}{2} + \frac{\int \frac{x^{2} \tan{\left(x \right)}}{\sqrt{- \left(x \tan{\left(x \right)} - 1\right) \left(x \tan{\left(x \right)} + 1\right)}}\, dx}{2} + \frac{\int \frac{x^{3} \tan^{2}{\left(x \right)}}{\sqrt{- \left(x \tan{\left(x \right)} - 1\right) \left(x \tan{\left(x \right)} + 1\right)}}\, dx}{2}
Simplificar
Respuesta numérica [src] 
(0.394257460195448 + 0.0864310318714141j)
(0.394257460195448 + 0.0864310318714141j)

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

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