Интеграл sin(2*x^2) (dx)

Вы ввели

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

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

Ответ

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

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

Численный ответ

0.498811855662711

Ответ (Неопределённый)

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

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