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

Вы ввели

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

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

Численный ответ

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

Рациональный знаменатель

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

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

Объединение рациональных выражений

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

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

Общее упрощение

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

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

Собрать выражение

 1 + atan(x)           atan(x) /     2\        
x           *log(x) + x       *\1 + x /*atan(x)
-----------------------------------------------
                          3                    
                     x + x                     

$$\frac{1}{x^{3} + x} \left(x^{\operatorname{atan}{\left (x \right )} + 1} \log{\left (x \right )} + x^{\operatorname{atan}{\left (x \right )}} \left(x^{2} + 1\right) \operatorname{atan}{\left (x \right )}\right)$$

Комбинаторика

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

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

Общий знаменатель

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

$$\frac{1}{x^{3} + x} \left(x^{2} x^{\operatorname{atan}{\left (x \right )}} \operatorname{atan}{\left (x \right )} + x x^{\operatorname{atan}{\left (x \right )}} \log{\left (x \right )} + x^{\operatorname{atan}{\left (x \right )}} \operatorname{atan}{\left (x \right )}\right)$$