Интеграл (x^4-2*x^2+2)/(x^2-2*x+2)^2 (dx)

Вы ввели

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[text]

  1                   
  /                   
 |                    
 |    4      2        
 |   x  - 2*x  + 2    
 |  --------------- dx
 |                2   
 |  / 2          \    
 |  \x  - 2*x + 2/    
 |                    
/                     
0                     

$$\int_{0}^{1} \frac{x^{4} - 2 x^{2} + 2}{\left(x^{2} - 2 x + 2\right)^{2}}\, dx$$

Ответ

[TeX]

[pretty]

[text]

  1                                       
  /                                       
 |                                        
 |    4      2                            
 |   x  - 2*x  + 2       3              pi
 |  --------------- dx = - - 2*log(2) + --
 |                2      2              4 
 |  / 2          \                        
 |  \x  - 2*x + 2/                        
 |                                        
/                                         
0                                         

$$-2\,\log 2+{{\pi}\over{4}}+{{3}\over{2}}$$

Численный ответ

[pretty]

[text]

0.899103802277558