Интеграл cos(25*x^2) (dx)

Вы ввели

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

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

Ответ

                                         /    ___\           
  1                   ___   ____         |5*\/ 2 |           
  /                 \/ 2 *\/ pi *fresnelc|-------|*gamma(1/4)
 |                                       |   ____|           
 |     /    2\                           \ \/ pi /           
 |  cos\25*x / dx = -----------------------------------------
 |                                40*gamma(5/4)              
/                                                            
0                                                            

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

Численный ответ

0.122293353279293

Ответ (Неопределённый)

                                            /      ___\           
                         ___   ____         |5*x*\/ 2 |           
  /                    \/ 2 *\/ pi *fresnelc|---------|*gamma(1/4)
 |                                          |    ____ |           
 |    /    2\                               \  \/ pi  /           
 | cos\25*x / dx = C + -------------------------------------------
 |                                    40*gamma(5/4)               
/                                                                 

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