Интеграл cos(4*x^2) (dx)

Вы ввели

  1             
  /             
 |              
 |     /   2\   
 |  cos\4*x / dx
 |              
/               
0               

$$\int_{0}^{1} \cos{\left (4 x^{2} \right )}\, dx$$

Ответ

                                        /    ___\           
  1                  ___   ____         |2*\/ 2 |           
  /                \/ 2 *\/ pi *fresnelc|-------|*gamma(1/4)
 |                                      |   ____|           
 |     /   2\                           \ \/ pi /           
 |  cos\4*x / dx = -----------------------------------------
 |                               16*gamma(5/4)              
/                                                           
0                                                           

$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(\sqrt{2}\,i+\sqrt{2}\right)+\left(\sqrt{2}\,i+ \sqrt{2}\right)\,\mathrm{erf}\left(\sqrt{2}\,i-\sqrt{2}\right)+ \left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(2\,\sqrt{-i} \right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(2\, \left(-1\right)^{{{1}\over{4}}}\right)\right)}\over{32}}$$

Ответ (Неопределённый)

                                           /      ___\           
                        ___   ____         |2*x*\/ 2 |           
  /                   \/ 2 *\/ pi *fresnelc|---------|*gamma(1/4)
 |                                         |    ____ |           
 |    /   2\                               \  \/ pi  /           
 | cos\4*x / dx = C + -------------------------------------------
 |                                   16*gamma(5/4)               
/                                                                

$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,x\right)+\left( -\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(\left(\sqrt{2}- \sqrt{2}\,i\right)\,x\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(2\,\sqrt{-i}\,x\right)+\left(\sqrt{2}\,i-\sqrt{2} \right)\,\mathrm{erf}\left(2\,\left(-1\right)^{{{1}\over{4}}}\,x \right)\right)}\over{32}}$$