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Resolución de integrales/ cos(x^10)

Integral de cos(x^10) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo            
  /            
 |             
 |     / 10\   
 |  cos\x  / dx
 |             
/              
2
$$\int\limits_{2}^{\infty} \cos{\left(x^{10} \right)}\, dx$$ 
Integral(cos(x^10), (x, 2, oo))
Respuesta (Indefinida) [src] 
                                                         
                                     _  /  1/20  |   20 \
                                    |_  |        | -x   |
  /                  x*Gamma(1/20)* |   |     21 | -----|
 |                                 1  2 |1/2, -- |   4  |
 |    / 10\                             \     20 |      /
 | cos\x  / dx = C + ------------------------------------
 |                                       /21\            
/                                20*Gamma|--|            
                                         \20/
$$\int \cos{\left(x^{10} \right)}\, dx = C + \frac{x \Gamma\left(\frac{1}{20}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{20} \\ \frac{1}{2}, \frac{21}{20} \end{matrix}\middle| {- \frac{x^{20}}{4}} \right)}}{20 \Gamma\left(\frac{21}{20}\right)}$$
Simplificar
Respuesta [src] 
       /                                                         \
       |                                   _  /  1/20  |        \|
       |                                  |_  |        |        ||
       |                    Gamma(-1/20)* |   |     21 | -262144||
       |10___                            1  2 |1/2, -- |        ||
  ____ |\/ 2 *Gamma(1/20)                     \     20 |        /|
\/ pi *|----------------- + -------------------------------------|
       |  2*Gamma(9/20)                  ____      /19\          |
       |                               \/ pi *Gamma|--|          |
       \                                           \20/          /
------------------------------------------------------------------
                                10
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{20}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{20} \\ \frac{1}{2}, \frac{21}{20} \end{matrix}\middle| {-262144} \right)}}{\sqrt{\pi} \Gamma\left(\frac{19}{20}\right)} + \frac{\sqrt[10]{2} \Gamma\left(\frac{1}{20}\right)}{2 \Gamma\left(\frac{9}{20}\right)}\right)}{10}$$ 
=
= 
       /                                                         \
       |                                   _  /  1/20  |        \|
       |                                  |_  |        |        ||
       |                    Gamma(-1/20)* |   |     21 | -262144||
       |10___                            1  2 |1/2, -- |        ||
  ____ |\/ 2 *Gamma(1/20)                     \     20 |        /|
\/ pi *|----------------- + -------------------------------------|
       |  2*Gamma(9/20)                  ____      /19\          |
       |                               \/ pi *Gamma|--|          |
       \                                           \20/          /
------------------------------------------------------------------
                                10
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{20}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{20} \\ \frac{1}{2}, \frac{21}{20} \end{matrix}\middle| {-262144} \right)}}{\sqrt{\pi} \Gamma\left(\frac{19}{20}\right)} + \frac{\sqrt[10]{2} \Gamma\left(\frac{1}{20}\right)}{2 \Gamma\left(\frac{9}{20}\right)}\right)}{10}$$ 
sqrt(pi)*(2^(1/10)*gamma(1/20)/(2*gamma(9/20)) + gamma(-1/20)*hyper((1/20,), (1/2, 21/20), -262144)/(sqrt(pi)*gamma(19/20)))/10

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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