Sr Examen
Integral de exp(-(x+p/(2x))^2+p) dx
Solución
Ha introducido
[src]
oo / | | 2 | / p \ | - |x + ---| + p | \ 2*x/ | e dx | / 0
$$\int\limits_{0}^{\infty} e^{p - \left(\frac{p}{2 x} + x\right)^{2}}\, dx$$
Integral(exp(-(x + p/((2*x)))^2 + p), (x, 0, oo))
Respuesta
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/ ____ ____ |\/ pi *cosh(p) \/ pi *sinh(p) pi |-------------- - -------------- for 2*|arg(p)| <= -- | 2 2 2 | | oo | / | | < | 2 | | / p \ | | p - |x + ---| | | \ 2*x/ | | e dx otherwise | | | / | 0 \
$$\begin{cases} - \frac{\sqrt{\pi} \sinh{\left(p \right)}}{2} + \frac{\sqrt{\pi} \cosh{\left(p \right)}}{2} & \text{for}\: 2 \left|{\arg{\left(p \right)}}\right| \leq \frac{\pi}{2} \\\int\limits_{0}^{\infty} e^{p - \left(\frac{p}{2 x} + x\right)^{2}}\, dx & \text{otherwise} \end{cases}$$
=
=
/ ____ ____ |\/ pi *cosh(p) \/ pi *sinh(p) pi |-------------- - -------------- for 2*|arg(p)| <= -- | 2 2 2 | | oo | / | | < | 2 | | / p \ | | p - |x + ---| | | \ 2*x/ | | e dx otherwise | | | / | 0 \
$$\begin{cases} - \frac{\sqrt{\pi} \sinh{\left(p \right)}}{2} + \frac{\sqrt{\pi} \cosh{\left(p \right)}}{2} & \text{for}\: 2 \left|{\arg{\left(p \right)}}\right| \leq \frac{\pi}{2} \\\int\limits_{0}^{\infty} e^{p - \left(\frac{p}{2 x} + x\right)^{2}}\, dx & \text{otherwise} \end{cases}$$
Piecewise((sqrt(pi)*cosh(p)/2 - sqrt(pi)*sinh(p)/2, 2*Abs(arg(p)) <= pi/2), (Integral(exp(p - (x + p/(2*x))^2), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.