Sr Examen
Integral de e^(t*(-2)*x+x^2/2) dx
Solución
Ha introducido
[src]
1 / | | 2 | x | t*(-2)*x + -- | 2 | E dx | / 0
$$\int\limits_{0}^{1} e^{x \left(-2\right) t + \frac{x^{2}}{2}}\, dx$$
Integral(E^((t*(-2))*x + x^2/2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 2 / ___\ 2 | x ___ ____ | ___ x*\/ 2 | -2*t | t*(-2)*x + -- \/ 2 *\/ pi *erfi|t*\/ 2 - -------|*e | 2 \ 2 / | E dx = C - ------------------------------------------- | 2 /
$$\int e^{x \left(-2\right) t + \frac{x^{2}}{2}}\, dx = C - \frac{\sqrt{2} \sqrt{\pi} e^{- 2 t^{2}} \operatorname{erfi}{\left(\sqrt{2} t - \frac{\sqrt{2} x}{2} \right)}}{2}$$
Respuesta
[src]
/ ___ \ 2
2 ___ ____ | \/ 2 ___| -2*t
___ ____ / ___\ -2*t \/ 2 *\/ pi *erfi|- ----- + t*\/ 2 |*e
\/ 2 *\/ pi *erfi\t*\/ 2 /*e \ 2 /
--------------------------------- - -------------------------------------------
2 2
$$\frac{\sqrt{2} \sqrt{\pi} e^{- 2 t^{2}} \operatorname{erfi}{\left(\sqrt{2} t \right)}}{2} - \frac{\sqrt{2} \sqrt{\pi} e^{- 2 t^{2}} \operatorname{erfi}{\left(\sqrt{2} t - \frac{\sqrt{2}}{2} \right)}}{2}$$
=
=
/ ___ \ 2
2 ___ ____ | \/ 2 ___| -2*t
___ ____ / ___\ -2*t \/ 2 *\/ pi *erfi|- ----- + t*\/ 2 |*e
\/ 2 *\/ pi *erfi\t*\/ 2 /*e \ 2 /
--------------------------------- - -------------------------------------------
2 2
$$\frac{\sqrt{2} \sqrt{\pi} e^{- 2 t^{2}} \operatorname{erfi}{\left(\sqrt{2} t \right)}}{2} - \frac{\sqrt{2} \sqrt{\pi} e^{- 2 t^{2}} \operatorname{erfi}{\left(\sqrt{2} t - \frac{\sqrt{2}}{2} \right)}}{2}$$
sqrt(2)*sqrt(pi)*erfi(t*sqrt(2))*exp(-2*t^2)/2 - sqrt(2)*sqrt(pi)*erfi(-sqrt(2)/2 + t*sqrt(2))*exp(-2*t^2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.