Sr Examen
Integral de x^(-1/2)*e^(-i*x*y) dx
Solución
Ha introducido
[src]
oo / | | -I*x*y | E | ------- dx | ___ | \/ x | / 0
$$\int\limits_{0}^{\infty} \frac{e^{y - i x}}{\sqrt{x}}\, dx$$
Integral(E^(((-i)*x)*y)/sqrt(x), (x, 0, oo))
Solución detallada
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Añadimos la constante de integración:
UpperGammaRule(a=-I*y, e=-1/2, context=E**(y*((-I)*x))/sqrt(x), symbol=x)
Respuesta:
Respuesta (Indefinida)
[src]
/ | | -I*x*y ____ _______ / _______\ | E I*\/ pi *\/ I*x*y *erfc\\/ I*x*y / | ------- dx = C + ---------------------------------- | ___ ___ | \/ x \/ x *y | /
$$\int \frac{e^{y - i x}}{\sqrt{x}}\, dx = C + \frac{i \sqrt{\pi} \sqrt{i x y} \operatorname{erfc}{\left(\sqrt{i x y} \right)}}{\sqrt{x} y}$$
Respuesta
[src]
/ pi*I | ---- | ____ _______________ 4 |-I*\/ pi *\/ polar_lift(y) *e |pi | pi |---------------------------------- for |-- + arg(y)| <= -- | y |2 | 2 | | oo | / < | | | -I*x*y | | e | | ------- dx otherwise | | ___ | | \/ x | | | / | 0 \
$$\begin{cases} - \frac{i \sqrt{\pi} e^{\frac{i \pi}{4}} \sqrt{\operatorname{polar\_lift}{\left(y \right)}}}{y} & \text{for}\: \left|{\arg{\left(y \right)} + \frac{\pi}{2}}\right| \leq \frac{\pi}{2} \\\int\limits_{0}^{\infty} \frac{e^{- i x y}}{\sqrt{x}}\, dx & \text{otherwise} \end{cases}$$
=
=
/ pi*I | ---- | ____ _______________ 4 |-I*\/ pi *\/ polar_lift(y) *e |pi | pi |---------------------------------- for |-- + arg(y)| <= -- | y |2 | 2 | | oo | / < | | | -I*x*y | | e | | ------- dx otherwise | | ___ | | \/ x | | | / | 0 \
$$\begin{cases} - \frac{i \sqrt{\pi} e^{\frac{i \pi}{4}} \sqrt{\operatorname{polar\_lift}{\left(y \right)}}}{y} & \text{for}\: \left|{\arg{\left(y \right)} + \frac{\pi}{2}}\right| \leq \frac{\pi}{2} \\\int\limits_{0}^{\infty} \frac{e^{- i x y}}{\sqrt{x}}\, dx & \text{otherwise} \end{cases}$$
Piecewise((-i*sqrt(pi)*sqrt(polar_lift(y))*exp(pi*i/4)/y, Abs(pi/2 + arg(y)) <= pi/2), (Integral(exp(-i*x*y)/sqrt(x), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.