Интеграл log(a*x+b) (dx)

Вы ввели

  1                
  /                
 |                 
 |  log(a*x + b) dx
 |                 
/                  
0                  

$$\int_{0}^{1} \log{\left (a x + b \right )}\, dx$$

Ответ

  1                                                                 
  /                                                                 
 |                        /1   b*log(a + b)\   b*log(b)             
 |  log(a*x + b) dx = - a*|- - ------------| - -------- + log(a + b)
 |                        |a         2     |      a                 
/                         \         a      /                        
0                                                                   

$$\int_{0}^{1} \log{\left (a x + b \right )}\, dx = - a \left(\frac{1}{a} - \frac{b}{a^{2}} \log{\left (a + b \right )}\right) + \log{\left (a + b \right )} - \frac{b}{a} \log{\left (b \right )}$$

Ответ (Неопределённый)

  /                      //            x*log(b)               for a = 0\
 |                       ||                                            |
 | log(a*x + b) dx = C + |<-b + (a*x + b)*log(a*x + b) - a*x           |
 |                       ||---------------------------------  otherwise|
/                        \\                a                           /

$${{\left(a\,x+b\right)\,\log \left(a\,x+b\right)-a\,x-b}\over{a}}$$