Интеграл 1/(e^(2*x)^(1/2)-1) (dx)

Вы ввели

  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |     _____       
 |   \/ 2*x        
 |  E        - 1   
 |                 
/                  
0                  

$$\int_{0}^{1} \frac{1}{e^{\sqrt{2 x}} - 1}\, dx$$

Ответ

  1                     1                     
  /                     /                     
 |                     |                      
 |       1             |          1           
 |  ------------ dx =  |  ----------------- dx
 |     _____           |          ___   ___   
 |   \/ 2*x            |        \/ 2 *\/ x    
 |  E        - 1       |  -1 + e              
 |                     |                      
/                     /                       
0                     0                       

$${{{\it li}_{2}(e^{\sqrt{2}\,\log E})+\sqrt{2}\,\log E\,\log \left(1 -e^{\sqrt{2}\,\log E}\right)-\left(\log E\right)^2}\over{\left(\log E\right)^2}}-{{\pi^2}\over{6\,\left(\log E\right)^2}}$$

Ответ (Неопределённый)

$$2\,\left({{{\it li}_{2}(e^{\sqrt{2}\,\log E\,\sqrt{x}})+\sqrt{2}\, \log E\,\sqrt{x}\,\log \left(1-e^{\sqrt{2}\,\log E\,\sqrt{x}}\right) }\over{2\,\left(\log E\right)^2}}-{{x}\over{2}}\right)$$