Интеграл cos(x^4) (dx)

Вы ввели

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

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

Ответ

  1                           _                   
  /                          |_  /  1/8    |     \
 |               gamma(1/8)* |   |         | -1/4|
 |     / 4\                 1  2 \1/2, 9/8 |     /
 |  cos\x / dx = ---------------------------------
 |                          8*gamma(9/8)          
/                                                 
0                                                 

$${{i\,\Gamma\left({{1}\over{4}} , i\right)\,\sin \left({{\pi}\over{8 }}\right)}\over{8}}-{{i\,\Gamma\left({{1}\over{4}} , -i\right)\, \sin \left({{\pi}\over{8}}\right)}\over{8}}-{{\Gamma\left({{1}\over{ 4}} , i\right)\,\cos \left({{\pi}\over{8}}\right)}\over{8}}-{{\Gamma \left({{1}\over{4}} , -i\right)\,\cos \left({{\pi}\over{8}}\right) }\over{8}}+{{\Gamma\left({{1}\over{4}}\right)\,\cos \left({{\pi }\over{8}}\right)}\over{4}}$$

Численный ответ

0.946840614165405

Ответ (Неопределённый)

                                                       
                                   _  /         |   8 \
  /                               |_  |  1/8    | -x  |
 |                  x*gamma(1/8)* |   |         | ----|
 |    / 4\                       1  2 \1/2, 9/8 |  4  /
 | cos\x / dx = C + -----------------------------------
 |                              8*gamma(9/8)           
/                                                      

$${{\left(\left(i\,\Gamma\left({{1}\over{4}} , i\,x^4\right)-i\, \Gamma\left({{1}\over{4}} , -i\,x^4\right)\right)\,\sin \left({{\pi }\over{8}}\right)+\left(-\Gamma\left({{1}\over{4}} , i\,x^4\right)- \Gamma\left({{1}\over{4}} , -i\,x^4\right)\right)\,\cos \left({{\pi }\over{8}}\right)\right)\,x}\over{8\,\left| x\right| }}$$