Sr Examen
Integral de x^(5/2)*e^((x*(-const))) dx
Solución
Ha introducido
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oo / | | 5/2 x*(-c) | x *E dx | / 0
$$\int\limits_{0}^{\infty} e^{- c x} x^{\frac{5}{2}}\, dx$$
Integral(x^(5/2)*E^(x*(-c)), (x, 0, oo))
Respuesta (Indefinida)
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/ ____ / _____\ \ / 5/2 |15*\/ pi *erfc\\/ c*x / _____ /15 2 2 5*c*x\ -c*x| | x *|----------------------- + \/ c*x *|-- + c *x + -----|*e | | 5/2 x*(-c) \ 8 \4 2 / / | x *E dx = C - ------------------------------------------------------------------- | 5/2 / c*(c*x)
$$\int e^{- c x} x^{\frac{5}{2}}\, dx = C - \frac{x^{\frac{5}{2}} \left(\sqrt{c x} \left(c^{2} x^{2} + \frac{5 c x}{2} + \frac{15}{4}\right) e^{- c x} + \frac{15 \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{c x} \right)}}{8}\right)}{c \left(c x\right)^{\frac{5}{2}}}$$
Respuesta
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/ ____ | 15*\/ pi pi | --------- for |arg(c)| < -- | 7/2 2 | 8*c | | oo < / | | | | 5/2 -c*x | | x *e dx otherwise | | |/ |0 \
$$\begin{cases} \frac{15 \sqrt{\pi}}{8 c^{\frac{7}{2}}} & \text{for}\: \left|{\arg{\left(c \right)}}\right| < \frac{\pi}{2} \\\int\limits_{0}^{\infty} x^{\frac{5}{2}} e^{- c x}\, dx & \text{otherwise} \end{cases}$$
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/ ____ | 15*\/ pi pi | --------- for |arg(c)| < -- | 7/2 2 | 8*c | | oo < / | | | | 5/2 -c*x | | x *e dx otherwise | | |/ |0 \
$$\begin{cases} \frac{15 \sqrt{\pi}}{8 c^{\frac{7}{2}}} & \text{for}\: \left|{\arg{\left(c \right)}}\right| < \frac{\pi}{2} \\\int\limits_{0}^{\infty} x^{\frac{5}{2}} e^{- c x}\, dx & \text{otherwise} \end{cases}$$
Piecewise((15*sqrt(pi)/(8*c^(7/2)), Abs(arg(c)) < pi/2), (Integral(x^(5/2)*exp(-c*x), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.