Sr Examen
Integral de (x^2cos^2x-4)exp(-2x^2)x dx
Solución
Ha introducido
[src]
oo / | | 2 | / 2 2 \ -2*x | \x *cos (x) - 4/*e *x dx | / 0
$$\int\limits_{0}^{\infty} x \left(x^{2} \cos^{2}{\left(x \right)} - 4\right) e^{- 2 x^{2}}\, dx$$
Integral(((x^2*cos(x)^2 - 4)*exp(-2*x^2))*x, (x, 0, oo))
Respuesta
[src]
/ / ___\ \
| ____ |I*\/ 2 | |
| \/ pi *erf|-------| ___ 1/2|
___ | \ 2 / I*\/ 2 *e | -1/2
I*\/ 2 *|- ------------------- + ------------|*e
31 \ 8 8 /
- -- - ----------------------------------------------------
32 4
$$- \frac{31}{32} - \frac{\sqrt{2} i \left(- \frac{\sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} i}{2} \right)}}{8} + \frac{\sqrt{2} i e^{\frac{1}{2}}}{8}\right)}{4 e^{\frac{1}{2}}}$$
=
=
/ / ___\ \
| ____ |I*\/ 2 | |
| \/ pi *erf|-------| ___ 1/2|
___ | \ 2 / I*\/ 2 *e | -1/2
I*\/ 2 *|- ------------------- + ------------|*e
31 \ 8 8 /
- -- - ----------------------------------------------------
32 4
$$- \frac{31}{32} - \frac{\sqrt{2} i \left(- \frac{\sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} i}{2} \right)}}{8} + \frac{\sqrt{2} i e^{\frac{1}{2}}}{8}\right)}{4 e^{\frac{1}{2}}}$$
-31/32 - i*sqrt(2)*(-sqrt(pi)*erf(i*sqrt(2)/2)/8 + i*sqrt(2)*exp(1/2)/8)*exp(-1/2)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.