Интеграл x/(a+b*x) (dx)

Вы ввели

[TeX]

[pretty]

[text]

  1           
  /           
 |            
 |     x      
 |  ------- dx
 |  a + b*x   
 |            
/             
0             

$$\int_{0}^{1} \frac{x}{a + b x}\, dx$$

Ответ

[TeX]

[pretty]

[text]

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

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

Ответ (Неопределённый)

[TeX]

[pretty]

[text]

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

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

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