Интеграл sin(100*x^2) (dx)

Вы ввели

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

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

Ответ

                                            /     ___\           
  1                      ___   ____         |10*\/ 2 |           
  /                  3*\/ 2 *\/ pi *fresnels|--------|*gamma(3/4)
 |                                          |   ____ |           
 |     /     2\                             \ \/ pi  /           
 |  sin\100*x / dx = --------------------------------------------
 |                                  80*gamma(7/4)                
/                                                                
0                                                                

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

Численный ответ

0.0583670899929623

Ответ (Неопределённый)

                                               /       ___\           
                            ___   ____         |10*x*\/ 2 |           
  /                     3*\/ 2 *\/ pi *fresnels|----------|*gamma(3/4)
 |                                             |    ____  |           
 |    /     2\                                 \  \/ pi   /           
 | sin\100*x / dx = C + ----------------------------------------------
 |                                      80*gamma(7/4)                 
/                                                                     

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