Интеграл sin(25*x^2) (dx)

Вы ввели

  1              
  /              
 |               
 |     /    2\   
 |  sin\25*x / dx
 |               
/                
0                

$$\int_{0}^{1} \sin{\left (25 x^{2} \right )}\, dx$$

Ответ

                                           /    ___\           
  1                     ___   ____         |5*\/ 2 |           
  /                 3*\/ 2 *\/ pi *fresnels|-------|*gamma(3/4)
 |                                         |   ____|           
 |     /    2\                             \ \/ pi /           
 |  sin\25*x / dx = -------------------------------------------
 |                                 40*gamma(7/4)               
/                                                              
0                                                              

$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf} \left({{5\,\sqrt{2}\,i+5\,\sqrt{2}}\over{2}}\right)+\left(\sqrt{2}\, i-\sqrt{2}\right)\,\mathrm{erf}\left({{5\,\sqrt{2}\,i-5\,\sqrt{2} }\over{2}}\right)+\left(\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf} \left(5\,\sqrt{-i}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\, \mathrm{erf}\left(5\,\left(-1\right)^{{{1}\over{4}}}\right)\right) }\over{80}}$$

Численный ответ

0.105583456233064

Ответ (Неопределённый)

                                              /      ___\           
                           ___   ____         |5*x*\/ 2 |           
  /                    3*\/ 2 *\/ pi *fresnels|---------|*gamma(3/4)
 |                                            |    ____ |           
 |    /    2\                                 \  \/ pi  /           
 | sin\25*x / dx = C + ---------------------------------------------
 |                                     40*gamma(7/4)                
/                                                                   

$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf} \left({{\left(5\,\sqrt{2}\,i+5\,\sqrt{2}\right)\,x}\over{2}}\right)+ \left(\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left({{\left(5\, \sqrt{2}\,i-5\,\sqrt{2}\right)\,x}\over{2}}\right)+\left(\sqrt{2}- \sqrt{2}\,i\right)\,\mathrm{erf}\left(5\,\sqrt{-i}\,x\right)+\left( \sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left(5\,\left(-1\right)^{ {{1}\over{4}}}\,x\right)\right)}\over{80}}$$