Интеграл sin(x*x) (dx)

Вы ввели

  1            
  /            
 |             
 |  sin(x*x) dx
 |             
/              
0              

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

Ответ

                                         /  ___ \           
                      ___   ____         |\/ 2  |           
  1               3*\/ 2 *\/ pi *fresnels|------|*gamma(3/4)
  /                                      |  ____|           
 |                                       \\/ pi /           
 |  sin(x*x) dx = ------------------------------------------
 |                               8*gamma(7/4)               
/                                                           
0                                                           

$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf} \left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left(\sqrt{2}\,i- \sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2}}\over{2}} \right)+\left(\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}\left(\sqrt{- i}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left( \left(-1\right)^{{{1}\over{4}}}\right)\right)}\over{16}}$$

Численный ответ

0.310268301723381

Ответ (Неопределённый)

                                            /    ___\           
                         ___   ____         |x*\/ 2 |           
                     3*\/ 2 *\/ pi *fresnels|-------|*gamma(3/4)
  /                                         |   ____|           
 |                                          \ \/ pi /           
 | sin(x*x) dx = C + -------------------------------------------
 |                                   8*gamma(7/4)               
/                                                               

$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf} \left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,x}\over{2}}\right)+\left( \sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i- \sqrt{2}\right)\,x}\over{2}}\right)+\left(\sqrt{2}-\sqrt{2}\,i \right)\,\mathrm{erf}\left(\sqrt{-i}\,x\right)+\left(\sqrt{2}\,i+ \sqrt{2}\right)\,\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\, x\right)\right)}\over{16}}$$