Sr Examen
Integral de (2x+3)e^-((x-3)(x+1)) dx
Solución
Ha introducido
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oo / | | -(x - 3)*(x + 1) | (2*x + 3)*E dx | / -oo
$$\int\limits_{-\infty}^{\infty} e^{- \left(x - 3\right) \left(x + 1\right)} \left(2 x + 3\right)\, dx$$
Integral((2*x + 3)*E^(-(x - 3)*(x + 1)), (x, -oo, oo))
Respuesta (Indefinida)
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/ / / \ / | | | | | | | 2 | 2 | | -(x - 3)*(x + 1) | | -x 2*x | -x 2*x | 3 | (2*x + 3)*E dx = C + |2* | x*e *e dx + 3* | e *e dx|*e | | | | | / \ / / /
$$\int e^{- \left(x - 3\right) \left(x + 1\right)} \left(2 x + 3\right)\, dx = C + \left(3 \int e^{2 x} e^{- x^{2}}\, dx + 2 \int x e^{2 x} e^{- x^{2}}\, dx\right) e^{3}$$
Respuesta
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____ 4 ____ 4
/ -4 ____ \ 4 / ____ -4\ 4 9*\/ pi *(2 - erfc(2))*e 9*\/ pi *erfc(2)*e
\- e - 2*\/ pi *(2 - erfc(2))/*e + \- 2*\/ pi *erfc(2) + e /*e + ------------------------- + -------------------
2 2
$$\left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) - e^{-4}\right) e^{4} + \left(- 2 \sqrt{\pi} \operatorname{erfc}{\left(2 \right)} + e^{-4}\right) e^{4} + \frac{9 \sqrt{\pi} e^{4} \operatorname{erfc}{\left(2 \right)}}{2} + \frac{9 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) e^{4}}{2}$$
=
=
____ 4 ____ 4
/ -4 ____ \ 4 / ____ -4\ 4 9*\/ pi *(2 - erfc(2))*e 9*\/ pi *erfc(2)*e
\- e - 2*\/ pi *(2 - erfc(2))/*e + \- 2*\/ pi *erfc(2) + e /*e + ------------------------- + -------------------
2 2
$$\left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) - e^{-4}\right) e^{4} + \left(- 2 \sqrt{\pi} \operatorname{erfc}{\left(2 \right)} + e^{-4}\right) e^{4} + \frac{9 \sqrt{\pi} e^{4} \operatorname{erfc}{\left(2 \right)}}{2} + \frac{9 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) e^{4}}{2}$$
(-exp(-4) - 2*sqrt(pi)*(2 - erfc(2)))*exp(4) + (-2*sqrt(pi)*erfc(2) + exp(-4))*exp(4) + 9*sqrt(pi)*(2 - erfc(2))*exp(4)/2 + 9*sqrt(pi)*erfc(2)*exp(4)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.