Интеграл x^2*a^x (dx)

Вы ввели

  1         
  /         
 |          
 |   2  x   
 |  x *a  dx
 |          
/           
0           

$$\int_{0}^{1} a^{x} x^{2}\, dx$$

Ответ

  1            /                                                        6       
  /            |                      1/3                        for log (a) = 0
 |             |                                                                
 |   2  x      |              /   5           4           3   \                 
 |  x *a  dx = <     2      a*\log (a) - 2*log (a) + 2*log (a)/                 
 |             |- ------- + -----------------------------------     otherwise   
/              |     3                       6                                  
0              |  log (a)                 log (a)                               
               \                                                                

$${{a\,\left(\log a\right)^2-2\,a\,\log a+2\,a}\over{\left(\log a \right)^3}}-{{2}\over{\left(\log a\right)^3}}$$

Ответ (Неопределённый)

                  //                    3                                     \
                  ||                   x                              6       |
  /               ||                   --                      for log (a) = 0|
 |                ||                   3                                      |
 |  2  x          ||                                                          |
 | x *a  dx = C + |< x /     3       2    5             4   \                 |
 |                ||a *\2*log (a) + x *log (a) - 2*x*log (a)/                 |
/                 ||-----------------------------------------     otherwise   |
                  ||                    6                                     |
                  ||                 log (a)                                  |
                  \\                                                          /

$${{\left(\left(\log a\right)^2\,x^2-2\,\log a\,x+2\right)\,e^{\log a \,x}}\over{\left(\log a\right)^3}}$$