Интеграл sqrt(a^2+x^2) (dx)

Вы ввели

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[pretty]

[text]

  1                
  /                
 |                 
 |     _________   
 |    /  2    2    
 |  \/  a  + x   dx
 |                 
/                  
0                  

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

Ответ

[TeX]

[pretty]

[text]

  1                          ________              
  /                         /     1                
 |                    a*   /  1 + --     2      /1\
 |     _________          /        2    a *asinh|-|
 |    /  2    2         \/        a             \a/
 |  \/  a  + x   dx = --------------- + -----------
 |                           2               2     
/                                                  
0                                                  

$$\int_{0}^{1} \sqrt{a^{2} + x^{2}}\, dx = \frac{a^{2}}{2} \operatorname{asinh}{\left (\frac{1}{a} \right )} + \frac{a}{2} \sqrt{1 + \frac{1}{a^{2}}}$$

Ответ (Неопределённый)

[TeX]

[pretty]

[text]

                                                 ________
                                                /      2 
  /                                            /      x  
 |                        2      /x\   a*x*   /   1 + -- 
 |    _________          a *asinh|-|         /         2 
 |   /  2    2                   \a/       \/         a  
 | \/  a  + x   dx = C + ----------- + ------------------
 |                            2                2         
/                                                        

$${{a^2\,{\rm asinh}\; \left({{x}\over{\left| a\right| }}\right) }\over{2}}+{{x\,\sqrt{x^2+a^2}}\over{2}}$$

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