Интеграл sin(3*x^2) (dx)

Вы ввели

  1             
  /             
 |              
 |     /   2\   
 |  sin\3*x / dx
 |              
/               
0               

$$\int_{0}^{1} \sin{\left (3 x^{2} \right )}\, dx$$

Ответ

                                        /  ___ \           
  1                  ___   ____         |\/ 6  |           
  /                \/ 6 *\/ pi *fresnels|------|*gamma(3/4)
 |                                      |  ____|           
 |     /   2\                           \\/ pi /           
 |  sin\3*x / dx = ----------------------------------------
 |                               8*gamma(7/4)              
/                                                          
0                                                          

$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3} \right)\,\mathrm{erf}\left({{\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3 }}\over{2}}\right)+\left(\sqrt{2}\,\sqrt{3}\,i-\sqrt{2}\,\sqrt{3} \right)\,\mathrm{erf}\left({{\sqrt{2}\,\sqrt{3}\,i-\sqrt{2}\,\sqrt{3 }}\over{2}}\right)+\left(\sqrt{2}\,\sqrt{3}-\sqrt{2}\,\sqrt{3}\,i \right)\,\mathrm{erf}\left(\sqrt{3}\,\sqrt{-i}\right)+\left(\sqrt{2} \,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3}\right)\,\mathrm{erf}\left(\left(-1 \right)^{{{1}\over{4}}}\,\sqrt{3}\right)\right)}\over{48}}$$

Численный ответ

0.514976174485537

Ответ (Неопределённый)

                                           /    ___\           
                        ___   ____         |x*\/ 6 |           
  /                   \/ 6 *\/ pi *fresnels|-------|*gamma(3/4)
 |                                         |   ____|           
 |    /   2\                               \ \/ pi /           
 | sin\3*x / dx = C + -----------------------------------------
 |                                   8*gamma(7/4)              
/                                                              

$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3} \right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\, \sqrt{3}\right)\,x}\over{2}}\right)+\left(\sqrt{2}\,\sqrt{3}\,i- \sqrt{2}\,\sqrt{3}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\, \sqrt{3}\,i-\sqrt{2}\,\sqrt{3}\right)\,x}\over{2}}\right)+\left( \sqrt{2}\,\sqrt{3}-\sqrt{2}\,\sqrt{3}\,i\right)\,\mathrm{erf}\left( \sqrt{3}\,\sqrt{-i}\,x\right)+\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\, \sqrt{3}\right)\,\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\, \sqrt{3}\,x\right)\right)}\over{48}}$$