Sr Examen
Integral de е^(i*t*x)(1-cosx)/(pi*x^2) dx
Solución
Ha introducido
[src]
1 / | | I*t*x | E *(1 - cos(x)) | ------------------- dx | 2 | pi*x | / 0
$$\int\limits_{0}^{1} \frac{e^{x i t} \left(1 - \cos{\left(x \right)}\right)}{\pi x^{2}}\, dx$$
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 | /
$$\int \frac{e^{x i t} \left(1 - \cos{\left(x \right)}\right)}{\pi x^{2}}\, dx = C - \frac{- i t \log{\left(t x \right)} + \frac{i t \log{\left(t^{2} x^{2} \right)}}{2} + \frac{i t \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} + \frac{i t \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} - \frac{t \operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} - \frac{t \operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} - \frac{i \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} + \frac{i \operatorname{Ci}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} + \frac{\operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 - \frac{1}{t} \right)} \right)}}{2} - \frac{\operatorname{Si}{\left(t x \operatorname{polar\_lift}{\left(1 + \frac{1}{t} \right)} \right)}}{2} - \frac{i \sin{\left(t x - x \right)}}{2 x} - \frac{i \sin{\left(t x + x \right)}}{2 x} - \frac{\cos{\left(t x - x \right)}}{2 x} - \frac{\cos{\left(t x + x \right)}}{2 x} + \frac{\operatorname{E}_{2}\left(- i t x\right)}{x}}{\pi}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.