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 definite integral
Сообщение20.06.2011, 09:09 
$\displaystyle{\int_{\alpha}^{\beta}\frac{\left(t^2-\alpha\beta\right).\ln\left(\frac{t}{\alpha}\right).\ln\left(\frac{t}{\beta}\right)}{\left(t^2+\alpha^2\right).\left(t^2+\beta^2\right)}dt}$

 
 
 
 Re: definite integral
Сообщение21.06.2011, 20:05 
Аватара пользователя
Quite obviously, this thing appeals for some creative substitution that would turn it to minus itself (and hence to 0).
Seems that $\xi={\alpha\beta\over t}$ would do.

 
 
 
 Re: definite integral
Сообщение30.06.2011, 07:35 
Look here : http://www.artofproblemsolving.com/Foru ... 7&t=415045

 
 
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