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Resolución de integrales/ (x^2)/ cos(x^2)/x^2

Integral de cos(x^2)/x^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo           
  /           
 |            
 |     / 2\   
 |  cos\x /   
 |  ------- dx
 |      2     
 |     x      
 |            
/             
1
$$\int\limits_{1}^{\infty} \frac{\cos{\left(x^{2} \right)}}{x^{2}}\, dx$$ 
Integral(cos(x^2)/x^2, (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                   /          
 |                   |           
 |    / 2\           |    / 2\   
 | cos\x /           | cos\x /   
 | ------- dx = C +  | ------- dx
 |     2             |     2     
 |    x              |    x      
 |                   |           
/                   /
$$\int \frac{\cos{\left(x^{2} \right)}}{x^{2}}\, dx = C + \int \frac{\cos{\left(x^{2} \right)}}{x^{2}}\, dx$$
Simplificar
Respuesta [src] 
       /                    /              /  ___ \         \           \
       |                    |  ___   ____  |\/ 2  |         |           |
       |                    |\/ 2 *\/ pi *S|------| + cos(1)|*Gamma(1/4)|
       |  ___               |              |  ____|         |           |
  ____ |\/ 2 *Gamma(-1/4)   \              \\/ pi /         /           |
\/ pi *|----------------- + --------------------------------------------|
       |   2*Gamma(3/4)                    ____                         |
       \                                 \/ pi *Gamma(5/4)              /
-------------------------------------------------------------------------
                                    4
$$\frac{\sqrt{\pi} \left(\frac{\sqrt{2} \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(1 \right)} + \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4}$$ 
=
= 
       /                    /              /  ___ \         \           \
       |                    |  ___   ____  |\/ 2  |         |           |
       |                    |\/ 2 *\/ pi *S|------| + cos(1)|*Gamma(1/4)|
       |  ___               |              |  ____|         |           |
  ____ |\/ 2 *Gamma(-1/4)   \              \\/ pi /         /           |
\/ pi *|----------------- + --------------------------------------------|
       |   2*Gamma(3/4)                    ____                         |
       \                                 \/ pi *Gamma(5/4)              /
-------------------------------------------------------------------------
                                    4
$$\frac{\sqrt{\pi} \left(\frac{\sqrt{2} \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(1 \right)} + \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4}$$ 
sqrt(pi)*(sqrt(2)*gamma(-1/4)/(2*gamma(3/4)) + (sqrt(2)*sqrt(pi)*fresnels(sqrt(2)/sqrt(pi)) + cos(1))*gamma(1/4)/(sqrt(pi)*gamma(5/4)))/4

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

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