Интеграл sin(x^2) (dx)

Вы ввели

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

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

Ответ

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

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