Sr Examen
Integral de e^(-6x^2+8x) dx
Solución
Ha introducido
[src]
oo / | | 2 | - 6*x + 8*x | E dx | / -oo
$$\int\limits_{-\infty}^{\infty} e^{- 6 x^{2} + 8 x}\, dx$$
Integral(E^(-6*x^2 + 8*x), (x, -oo, oo))
Respuesta (Indefinida)
[src]
/ / ___ \ | ___ ____ | 2*\/ 6 ___| 8/3 | 2 \/ 6 *\/ pi *erf|- ------- + x*\/ 6 |*e | - 6*x + 8*x \ 3 / | E dx = C + ------------------------------------------ | 12 /
$$\int e^{- 6 x^{2} + 8 x}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} e^{\frac{8}{3}} \operatorname{erf}{\left(\sqrt{6} x - \frac{2 \sqrt{6}}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
/ ___\
___ |2*\/ 6 | 8/3
___ 8/3 2*pi*\/ 6 *erf|-------|*e / / ___\\
2*pi*\/ 6 *e \ 3 / ___ ____ | |2*\/ 6 || 8/3
--------------- - ---------------------------- \/ 6 *\/ pi *|2 - erfc|-------||*e
3 3 \ \ 3 //
---------------------------------------------- + -------------------------------------
____ 12
8*\/ pi
$$\frac{- \frac{2 \sqrt{6} \pi e^{\frac{8}{3}} \operatorname{erf}{\left(\frac{2 \sqrt{6}}{3} \right)}}{3} + \frac{2 \sqrt{6} \pi e^{\frac{8}{3}}}{3}}{8 \sqrt{\pi}} + \frac{\sqrt{6} \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(\frac{2 \sqrt{6}}{3} \right)}\right) e^{\frac{8}{3}}}{12}$$
=
=
/ ___\
___ |2*\/ 6 | 8/3
___ 8/3 2*pi*\/ 6 *erf|-------|*e / / ___\\
2*pi*\/ 6 *e \ 3 / ___ ____ | |2*\/ 6 || 8/3
--------------- - ---------------------------- \/ 6 *\/ pi *|2 - erfc|-------||*e
3 3 \ \ 3 //
---------------------------------------------- + -------------------------------------
____ 12
8*\/ pi
$$\frac{- \frac{2 \sqrt{6} \pi e^{\frac{8}{3}} \operatorname{erf}{\left(\frac{2 \sqrt{6}}{3} \right)}}{3} + \frac{2 \sqrt{6} \pi e^{\frac{8}{3}}}{3}}{8 \sqrt{\pi}} + \frac{\sqrt{6} \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(\frac{2 \sqrt{6}}{3} \right)}\right) e^{\frac{8}{3}}}{12}$$
(2*pi*sqrt(6)*exp(8/3)/3 - 2*pi*sqrt(6)*erf(2*sqrt(6)/3)*exp(8/3)/3)/(8*sqrt(pi)) + sqrt(6)*sqrt(pi)*(2 - erfc(2*sqrt(6)/3))*exp(8/3)/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.