Sr Examen

Otras calculadoras

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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  pi           
  --           
  2            
   /           
  |            
  |     /1 \   
  |  cos|--| dx
  |     | 2|   
  |     \x /   
  |            
 /             
-pi            
----           
 2
∫−π2π2cos⁡(1x2) dx\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \cos{\left(\frac{1}{x^{2}} \right)}\, dx 
Integral(cos(x^(-2)), (x, -pi/2, pi/2))
Respuesta (Indefinida) [src] 
                                                          /   ___  \            
                         /1 \                 ___   ____  | \/ 2   |            
  /                 x*cos|--|*Gamma(-1/4)   \/ 2 *\/ pi *S|--------|*Gamma(-1/4)
 |                       | 2|                             |  ____  |            
 |    /1 \               \x /                             \\/ pi *x/            
 | cos|--| dx = C - --------------------- - ------------------------------------
 |    | 2|               4*Gamma(3/4)                   4*Gamma(3/4)            
 |    \x /                                                                      
 |                                                                              
/
∫cos⁡(1x2) dx=C−xcos⁡(1x2)Γ(−14)4Γ(34)−2πS(2πx)Γ(−14)4Γ(34)\int \cos{\left(\frac{1}{x^{2}} \right)}\, dx = C - \frac{x \cos{\left(\frac{1}{x^{2}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi} x}\right) \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)}
Simplificar
Gráfica
-1.50-1.25-1.00-0.75-0.50-0.250.000.250.500.751.001.251.505-5
Trazar el gráfico f(x)
Respuesta [src] 
                                          /    ___\            
        / 4 \                 ___   ____  |2*\/ 2 |            
  pi*cos|---|*Gamma(-1/4)   \/ 2 *\/ pi *S|-------|*Gamma(-1/4)
        |  2|                             |   3/2 |            
        \pi /                             \ pi    /            
- ----------------------- - -----------------------------------
        4*Gamma(3/4)                    2*Gamma(3/4)
−2πS(22π32)Γ(−14)2Γ(34)−πcos⁡(4π2)Γ(−14)4Γ(34)- \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2}}{\pi^{\frac{3}{2}}}\right) \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} - \frac{\pi \cos{\left(\frac{4}{\pi^{2}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} 
=
= 
                                          /    ___\            
        / 4 \                 ___   ____  |2*\/ 2 |            
  pi*cos|---|*Gamma(-1/4)   \/ 2 *\/ pi *S|-------|*Gamma(-1/4)
        |  2|                             |   3/2 |            
        \pi /                             \ pi    /            
- ----------------------- - -----------------------------------
        4*Gamma(3/4)                    2*Gamma(3/4)
−2πS(22π32)Γ(−14)2Γ(34)−πcos⁡(4π2)Γ(−14)4Γ(34)- \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2}}{\pi^{\frac{3}{2}}}\right) \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} - \frac{\pi \cos{\left(\frac{4}{\pi^{2}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} 
-pi*cos(4/pi^2)*gamma(-1/4)/(4*gamma(3/4)) - sqrt(2)*sqrt(pi)*fresnels(2*sqrt(2)/pi^(3/2))*gamma(-1/4)/(2*gamma(3/4))

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

    © Sr Examen – Калькулятор