Общий знаменатель 10*(-5/(1+5*x)^2-2*log(1+ ... 2*log(1+5*x))*exp(-5*x^2)

Вы ввели

                                                                       2
   /      5                           20*x        2             \  -5*x 
10*|- ---------- - 2*log(1 + 5*x) - ------- + 20*x *log(1 + 5*x)|*e     
   |           2                    1 + 5*x                     |       
   \  (1 + 5*x)                                                 /       

$$10 \left(20 x^{2} \log{\left (5 x + 1 \right )} + - \frac{20 x}{5 x + 1} + - 2 \log{\left (5 x + 1 \right )} - \frac{5}{\left(5 x + 1\right)^{2}}\right) e^{- 5 x^{2}}$$

Степени

                                                                      2
/      50                          200*x         2             \  -5*x 
|- ---------- - 20*log(1 + 5*x) - ------- + 200*x *log(1 + 5*x)|*e     
|           2                     1 + 5*x                      |       
\  (1 + 5*x)                                                   /       

$$\left(200 x^{2} \log{\left (5 x + 1 \right )} - \frac{200 x}{5 x + 1} - 20 \log{\left (5 x + 1 \right )} - \frac{50}{\left(5 x + 1\right)^{2}}\right) e^{- 5 x^{2}}$$

Численный ответ

10.0*(-2.0*log(1 + 5*x) - 5.0/(1.0 + 5.0*x)^2 + 20.0*x^2*log(1 + 5*x) - 20.0*x/(1.0 + 5.0*x))*exp(-5*x^2)

Объединение рациональных выражений

                                                                                          2
   /                                 2                    2          2             \  -5*x 
10*\-5 - 20*x*(1 + 5*x) - 2*(1 + 5*x) *log(1 + 5*x) + 20*x *(1 + 5*x) *log(1 + 5*x)/*e     
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                                                  2                                        
                                         (1 + 5*x)                                         

$$\frac{10 e^{- 5 x^{2}}}{\left(5 x + 1\right)^{2}} \left(20 x^{2} \left(5 x + 1\right)^{2} \log{\left (5 x + 1 \right )} - 20 x \left(5 x + 1\right) - 2 \left(5 x + 1\right)^{2} \log{\left (5 x + 1 \right )} - 5\right)$$

Общее упрощение

                                                                                2
/                             2               3 /         2\             \  -5*x 
\-50 - 250*x - 200*x*(1 + 5*x)  + 20*(1 + 5*x) *\-1 + 10*x /*log(1 + 5*x)/*e     
---------------------------------------------------------------------------------
                                             3                                   
                                    (1 + 5*x)                                    

$$\frac{e^{- 5 x^{2}}}{\left(5 x + 1\right)^{3}} \left(- 200 x \left(5 x + 1\right)^{2} - 250 x + 20 \left(5 x + 1\right)^{3} \left(10 x^{2} - 1\right) \log{\left (5 x + 1 \right )} - 50\right)$$

Собрать выражение

                                                                          2
/      50                           10*20*x          2             \  -5*x 
|- ---------- - 10*2*log(1 + 5*x) - ------- + 10*20*x *log(1 + 5*x)|*e     
|           2                       1 + 5*x                        |       
\  (1 + 5*x)                                                       /       

$$\left(- \frac{200 x}{5 x + 1} + 10 \cdot 20 x^{2} \log{\left (5 x + 1 \right )} - 20 \log{\left (5 x + 1 \right )} - \frac{50}{\left(5 x + 1\right)^{2}}\right) e^{- 5 x^{2}}$$

                                                                                                                                              2
/         /         20\     /          /         200\\    2 /           /         300\\    3    /         2000\    4    /         5000\\  -5*x 
\-50 - log\(1 + 5*x)  / + x*\-200 - log\(1 + 5*x)   // + x *\-1000 - log\(1 + 5*x)   // + x *log\(1 + 5*x)    / + x *log\(1 + 5*x)    //*e     
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                                                                               2                                                               
                                                                1 + 10*x + 25*x                                                                

$$\frac{e^{- 5 x^{2}}}{25 x^{2} + 10 x + 1} \left(x^{4} \log{\left (\left(5 x + 1\right)^{5000} \right )} + x^{3} \log{\left (\left(5 x + 1\right)^{2000} \right )} + x^{2} \left(- \log{\left (\left(5 x + 1\right)^{300} \right )} - 1000\right) + x \left(- \log{\left (\left(5 x + 1\right)^{200} \right )} - 200\right) - \log{\left (\left(5 x + 1\right)^{20} \right )} - 50\right)$$

Общий знаменатель

            2                                  2                                           3                      4             
-50 - 1000*x  - 200*x - 20*log(1 + 5*x) - 300*x *log(1 + 5*x) - 200*x*log(1 + 5*x) + 2000*x *log(1 + 5*x) + 5000*x *log(1 + 5*x)
--------------------------------------------------------------------------------------------------------------------------------
                                                         2             2       2                                                
                                                      5*x        2  5*x     5*x                                                 
                                                10*x*e     + 25*x *e     + e                                                    

$$\frac{1}{25 x^{2} e^{5 x^{2}} + 10 x e^{5 x^{2}} + e^{5 x^{2}}} \left(5000 x^{4} \log{\left (5 x + 1 \right )} + 2000 x^{3} \log{\left (5 x + 1 \right )} - 300 x^{2} \log{\left (5 x + 1 \right )} - 1000 x^{2} - 200 x \log{\left (5 x + 1 \right )} - 200 x - 20 \log{\left (5 x + 1 \right )} - 50\right)$$

Комбинаторика

                                                                                                                                   2
   /          2                               2                                         3                     4             \  -5*x 
10*\-5 - 100*x  - 20*x - 2*log(1 + 5*x) - 30*x *log(1 + 5*x) - 20*x*log(1 + 5*x) + 200*x *log(1 + 5*x) + 500*x *log(1 + 5*x)/*e     
------------------------------------------------------------------------------------------------------------------------------------
                                                                      2                                                             
                                                             (1 + 5*x)                                                              

$$\frac{10 e^{- 5 x^{2}}}{\left(5 x + 1\right)^{2}} \left(500 x^{4} \log{\left (5 x + 1 \right )} + 200 x^{3} \log{\left (5 x + 1 \right )} - 30 x^{2} \log{\left (5 x + 1 \right )} - 100 x^{2} - 20 x \log{\left (5 x + 1 \right )} - 20 x - 2 \log{\left (5 x + 1 \right )} - 5\right)$$

Раскрыть выражение

                                                                       2
   /      5                           20*x        2             \  -5*x 
10*|- ---------- - 2*log(1 + 5*x) - ------- + 20*x *log(1 + 5*x)|*e     
   |           2                    1 + 5*x                     |       
   \  (1 + 5*x)                                                 /       

$$10 \left(20 x^{2} \log{\left (5 x + 1 \right )} - \frac{20 x}{5 x + 1} - 2 \log{\left (5 x + 1 \right )} - \frac{5}{\left(5 x + 1\right)^{2}}\right) e^{- 5 x^{2}}$$