Descomposición de una fracción log(x)^atan(x)*(log(log(x))/(1+x²)+atan(x)/(x*log(x))) (logaritmo de (x) en el grado arco tangente de gente de (x) multiplicar por (logaritmo de (logaritmo de (x)) dividir por (1 más x al cuadrado) más arco tangente de gente de (x) dividir por (x multiplicar por logaritmo de (x))))

Ha introducido [src]

   atan(x)    /log(log(x))   atan(x) \
log       (x)*|----------- + --------|
              |        2     x*log(x)|
              \   1 + x              /

\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}}

log(x)^atan(x)*(log(log(x))/(1 + x^2) + atan(x)/((x*log(x))))

Simplificación general [src]

   -1 + atan(x)    //     2\                               \
log            (x)*\\1 + x /*atan(x) + x*log(x)*log(log(x))/
------------------------------------------------------------
                           /     2\                         
                         x*\1 + x /

\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)} - 1}}{x \left(x^{2} + 1\right)}

log(x)^(-1 + atan(x))*((1 + x^2)*atan(x) + x*log(x)*log(log(x)))/(x*(1 + x^2))

Respuesta numérica [src]

log(x)^atan(x)*(log(log(x))/(1.0 + x^2) + atan(x)/(x*log(x)))

log(x)^atan(x)*(log(log(x))/(1.0 + x^2) + atan(x)/(x*log(x)))

Combinatoria [src]

   atan(x)    / 2                                         \
log       (x)*\x *atan(x) + x*log(x)*log(log(x)) + atan(x)/
-----------------------------------------------------------
                       /     2\                            
                     x*\1 + x /*log(x)

\frac{\left(x^{2} \operatorname{atan}{\left(x \right)} + x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}}}{x \left(x^{2} + 1\right) \log{\left(x \right)}}

log(x)^atan(x)*(x^2*atan(x) + x*log(x)*log(log(x)) + atan(x))/(x*(1 + x^2)*log(x))

Denominador común [src]

   atan(x)               2    atan(x)                   atan(x)                      
log       (x)*atan(x) + x *log       (x)*atan(x) + x*log       (x)*log(x)*log(log(x))
-------------------------------------------------------------------------------------
                                             3                                       
                                 x*log(x) + x *log(x)

\frac{x^{2} \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}} \operatorname{atan}{\left(x \right)} + x \log{\left(x \right)} \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}} \log{\left(\log{\left(x \right)} \right)} + \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}} \operatorname{atan}{\left(x \right)}}{x^{3} \log{\left(x \right)} + x \log{\left(x \right)}}

(log(x)^atan(x)*atan(x) + x^2*log(x)^atan(x)*atan(x) + x*log(x)^atan(x)*log(x)*log(log(x)))/(x*log(x) + x^3*log(x))

Denominador racional [src]

   atan(x)    //     2\                               \
log       (x)*\\1 + x /*atan(x) + x*log(x)*log(log(x))/
-------------------------------------------------------
                     /     2\                          
                   x*\1 + x /*log(x)

\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}}}{x \left(x^{2} + 1\right) \log{\left(x \right)}}

log(x)^atan(x)*((1 + x^2)*atan(x) + x*log(x)*log(log(x)))/(x*(1 + x^2)*log(x))

Unión de expresiones racionales [src]

   atan(x)    //     2\                               \
log       (x)*\\1 + x /*atan(x) + x*log(x)*log(log(x))/
-------------------------------------------------------
                     /     2\                          
                   x*\1 + x /*log(x)

\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)}^{\operatorname{atan}{\left(x \right)}}}{x \left(x^{2} + 1\right) \log{\left(x \right)}}

log(x)^atan(x)*((1 + x^2)*atan(x) + x*log(x)*log(log(x)))/(x*(1 + x^2)*log(x))

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¿Cómo vas a descomponer esta log(x)^atan(x)(log(log(x))/(1+x^2)+atan(x)/(xlog(x))) expresión en fracciones?

Solución

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¿Cómo vas a descomponer esta log(x)^atan(x)*(log(log(x))/(1+x^2)+atan(x)/(x*log(x))) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta log(x)^atan(x)(log(log(x))/(1+x^2)+atan(x)/(xlog(x))) expresión en fracciones?