Sr Examen
Integral de e^(x*(-a))/(1+x^4) dx
Solución
Ha introducido
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oo / | | x*(-a) | E | ------- dx | 4 | 1 + x | / 0
$$\int\limits_{0}^{\infty} \frac{e^{- a x}}{x^{4} + 1}\, dx$$
Integral(E^(x*(-a))/(1 + x^4), (x, 0, oo))
Respuesta (Indefinida)
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/ / | | | x*(-a) | -a*x | E | e | ------- dx = C + | ------ dx | 4 | 4 | 1 + x | 1 + x | | / /
$$\int \frac{e^{- a x}}{x^{4} + 1}\, dx = C + \int \frac{e^{- a x}}{x^{4} + 1}\, dx$$
Respuesta
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/ / | 4 \ | ___ __5, 1 | 3/4 | polar_lift (a)| |\/ 2 */__ | | --------------| | \_|1, 5 \3/4, 0, 1/4, 1/2, 3/4 | 256 / |--------------------------------------------------------- for 4*|arg(a)| <= 2*pi | 3/2 | 8*pi | | oo < / | | | | -a*x | | e | | ------ dx otherwise | | 4 | | 1 + x | | | / \ 0
$$\begin{cases} \frac{\sqrt{2} {G_{1, 5}^{5, 1}\left(\begin{matrix} \frac{3}{4} & \\\frac{3}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & \end{matrix} \middle| {\frac{\operatorname{polar\_lift}^{4}{\left(a \right)}}{256}} \right)}}{8 \pi^{\frac{3}{2}}} & \text{for}\: 4 \left|{\arg{\left(a \right)}}\right| \leq 2 \pi \\\int\limits_{0}^{\infty} \frac{e^{- a x}}{x^{4} + 1}\, dx & \text{otherwise} \end{cases}$$
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/ / | 4 \ | ___ __5, 1 | 3/4 | polar_lift (a)| |\/ 2 */__ | | --------------| | \_|1, 5 \3/4, 0, 1/4, 1/2, 3/4 | 256 / |--------------------------------------------------------- for 4*|arg(a)| <= 2*pi | 3/2 | 8*pi | | oo < / | | | | -a*x | | e | | ------ dx otherwise | | 4 | | 1 + x | | | / \ 0
$$\begin{cases} \frac{\sqrt{2} {G_{1, 5}^{5, 1}\left(\begin{matrix} \frac{3}{4} & \\\frac{3}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & \end{matrix} \middle| {\frac{\operatorname{polar\_lift}^{4}{\left(a \right)}}{256}} \right)}}{8 \pi^{\frac{3}{2}}} & \text{for}\: 4 \left|{\arg{\left(a \right)}}\right| \leq 2 \pi \\\int\limits_{0}^{\infty} \frac{e^{- a x}}{x^{4} + 1}\, dx & \text{otherwise} \end{cases}$$
Piecewise((sqrt(2)*meijerg(((3/4,), ()), ((3/4, 0, 1/4, 1/2, 3/4), ()), polar_lift(a)^4/256)/(8*pi^(3/2)), 4*Abs(arg(a)) <= 2*pi), (Integral(exp(-a*x)/(1 + x^4), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.