Интеграл cos(100*x^2) (dx)

Вы ввели

  1               
  /               
 |                
 |     /     2\   
 |  cos\100*x / dx
 |                
/                 
0                 

$$\int_{0}^{1} \cos{\left (100 x^{2} \right )}\, dx$$

Ответ

                                          /     ___\           
  1                    ___   ____         |10*\/ 2 |           
  /                  \/ 2 *\/ pi *fresnelc|--------|*gamma(1/4)
 |                                        |   ____ |           
 |     /     2\                           \ \/ pi  /           
 |  cos\100*x / dx = ------------------------------------------
 |                                 80*gamma(5/4)               
/                                                              
0                                                              

$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(5\,\sqrt{2}\,i+5\,\sqrt{2}\right)+\left(\sqrt{2}\, i+\sqrt{2}\right)\,\mathrm{erf}\left(5\,\sqrt{2}\,i-5\,\sqrt{2} \right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(10\, \sqrt{-i}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf} \left(10\,\left(-1\right)^{{{1}\over{4}}}\right)\right)}\over{160}}$$

Численный ответ

0.0601125184813444

Ответ (Неопределённый)

                                             /       ___\           
                          ___   ____         |10*x*\/ 2 |           
  /                     \/ 2 *\/ pi *fresnelc|----------|*gamma(1/4)
 |                                           |    ____  |           
 |    /     2\                               \  \/ pi   /           
 | cos\100*x / dx = C + --------------------------------------------
 |                                     80*gamma(5/4)                
/                                                                   

$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(\left(5\,\sqrt{2}\,i+5\,\sqrt{2}\right)\,x\right)+ \left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(\left(5\, \sqrt{2}-5\,\sqrt{2}\,i\right)\,x\right)+\left(-\sqrt{2}\,i-\sqrt{2} \right)\,\mathrm{erf}\left(10\,\sqrt{-i}\,x\right)+\left(\sqrt{2}\,i -\sqrt{2}\right)\,\mathrm{erf}\left(10\,\left(-1\right)^{{{1}\over{4 }}}\,x\right)\right)}\over{160}}$$