Sr Examen
Integral de x^2*e^(a*x) dx
Solución
Ha introducido
[src]
1 / | | 2 a*x | x *E dx | / 0
$$\int\limits_{0}^{1} e^{a x} x^{2}\, dx$$
Integral(x^2*E^(a*x), (x, 0, 1))
Respuesta (Indefinida)
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/// 2 2 \ a*x \
||\2 + a *x - 2*a*x/*e 3 |
/ ||------------------------ for a != 0|
| || 3 |
| 2 a*x || a |
| x *E dx = C + |< |
| || 3 |
/ || x |
|| -- otherwise |
|| 3 |
\\ /
$$\int e^{a x} x^{2}\, dx = C + \begin{cases} \frac{\left(a^{2} x^{2} - 2 a x + 2\right) e^{a x}}{a^{3}} & \text{for}\: a^{3} \neq 0 \\\frac{x^{3}}{3} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ / 2 \ a | 2 \2 + a - 2*a/*e |- -- + ----------------- for And(a > -oo, a < oo, a != 0) < 3 3 | a a | \ 1/3 otherwise
$$\begin{cases} \frac{\left(a^{2} - 2 a + 2\right) e^{a}}{a^{3}} - \frac{2}{a^{3}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\frac{1}{3} & \text{otherwise} \end{cases}$$
=
=
/ / 2 \ a | 2 \2 + a - 2*a/*e |- -- + ----------------- for And(a > -oo, a < oo, a != 0) < 3 3 | a a | \ 1/3 otherwise
$$\begin{cases} \frac{\left(a^{2} - 2 a + 2\right) e^{a}}{a^{3}} - \frac{2}{a^{3}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\frac{1}{3} & \text{otherwise} \end{cases}$$
Piecewise((-2/a^3 + (2 + a^2 - 2*a)*exp(a)/a^3, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (1/3, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.