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Resolución de integrales/ -cosx/ pi*x^2/ е^(i*t*x)(1-cosx)/(pi*x^2)

Integral de е^(i*t*x)(1-cosx)/(pi*x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
 |                        
 |   I*t*x                
 |  E     *(1 - cos(x))   
 |  ------------------- dx
 |             2          
 |         pi*x           
 |                        
/                         
0
∫01exit(1−cos⁡(x))πx2 dx\int\limits_{0}^{1} \frac{e^{x i t} \left(1 - \cos{\left(x \right)}\right)}{\pi x^{2}}\, dx 
Integral((E^((i*t)*x)*(1 - cos(x)))/((pi*x^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                  /              /    1\\     /              /    1\\                           /              /    1\\       /              /    1\\       /              /    1\\       /              /    1\\                                        /              /    1\\         /              /    1\\                                                                   
  /                             Si|t*x*polar_lift|1 - -||   Si|t*x*polar_lift|1 + -||                       I*Ci|t*x*polar_lift|1 + -||   I*Ci|t*x*polar_lift|1 - -||   t*Si|t*x*polar_lift|1 + -||   t*Si|t*x*polar_lift|1 - -||                                  I*t*Ci|t*x*polar_lift|1 + -||   I*t*Ci|t*x*polar_lift|1 - -||          / 2  2\                                                  
 |                                \              \    t//     \              \    t//   expint(2, -I*t*x)       \              \    t//       \              \    t//       \              \    t//       \              \    t//   cos(x + t*x)   cos(-x + t*x)         \              \    t//         \              \    t//   I*t*log\t *x /                  I*sin(x + t*x)   I*sin(-x + t*x)
 |  I*t*x                       ------------------------- - ------------------------- + ----------------- + --------------------------- - --------------------------- - --------------------------- - --------------------------- - ------------ - ------------- + ----------------------------- + ----------------------------- + -------------- - I*t*log(t*x) - -------------- - ---------------
 | E     *(1 - cos(x))                      2                           2                       x                        2                             2                             2                             2                    2*x             2*x                      2                               2                       2                              2*x               2*x      
 | ------------------- dx = C - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |            2                                                                                                                                                                                                  pi                                                                                                                                                                                
 |        pi*x                                                                                                                                                                                                                                                                                                                                                                                     
 |                                                                                                                                                                                                                                                                                                                                                                                                 
/
∫exit(1−cos⁡(x))πx2 dx=C−−itlog⁡(tx)+itlog⁡(t2x2)2+itCi⁡(txpolar_lift⁡(1−1t))2+itCi⁡(txpolar_lift⁡(1+1t))2−tSi⁡(txpolar_lift⁡(1−1t))2−tSi⁡(txpolar_lift⁡(1+1t))2−iCi⁡(txpolar_lift⁡(1−1t))2+iCi⁡(txpolar_lift⁡(1+1t))2+Si⁡(txpolar_lift⁡(1−1t))2−Si⁡(txpolar_lift⁡(1+1t))2−isin⁡(tx−x)2x−isin⁡(tx+x)2x−cos⁡(tx−x)2x−cos⁡(tx+x)2x+E⁡2(−itx)xπ\int \frac{e^{x i t} \left(1 - \cos{\left(x \right)}\right)}{\pi x^{2}}\, dx = C - \frac{- i t \log{\left(t x \right)} + \frac{i t \log{\left(t^{2} x^{2} \right)}}{2} + \frac{i t \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} + \frac{i t \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} - \frac{t \operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} - \frac{t \operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} - \frac{i \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} + \frac{i \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} + \frac{\operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} - \frac{\operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} - \frac{i \sin{\left(t x - x \right)}}{2 x} - \frac{i \sin{\left(t x + x \right)}}{2 x} - \frac{\cos{\left(t x - x \right)}}{2 x} - \frac{\cos{\left(t x + x \right)}}{2 x} + \frac{\operatorname{E}_{2}\left(- i t x\right)}{x}}{\pi}
Simplificar

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

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