Sr Examen
Integral de x^3*e^(a*x) dx
Solución
Ha introducido
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1 / | | 3 a*x | x *E dx | / 0
$$\int\limits_{0}^{1} e^{a x} x^{3}\, dx$$
Integral(x^3*E^(a*x), (x, 0, 1))
Respuesta (Indefinida)
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/// 3 3 2 2 \ a*x \
||\-6 + a *x - 3*a *x + 6*a*x/*e 4 |
/ ||----------------------------------- for a != 0|
| || 4 |
| 3 a*x || a |
| x *E dx = C + |< |
| || 4 |
/ || x |
|| -- otherwise |
|| 4 |
\\ /
$$\int e^{a x} x^{3}\, dx = C + \begin{cases} \frac{\left(a^{3} x^{3} - 3 a^{2} x^{2} + 6 a x - 6\right) e^{a x}}{a^{4}} & \text{for}\: a^{4} \neq 0 \\\frac{x^{4}}{4} & \text{otherwise} \end{cases}$$
Respuesta
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/ / 3 2 \ a |6 \-6 + a - 3*a + 6*a/*e |-- + ------------------------- for And(a > -oo, a < oo, a != 0) < 4 4 |a a | \ 1/4 otherwise
$$\begin{cases} \frac{\left(a^{3} - 3 a^{2} + 6 a - 6\right) e^{a}}{a^{4}} + \frac{6}{a^{4}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\frac{1}{4} & \text{otherwise} \end{cases}$$
=
=
/ / 3 2 \ a |6 \-6 + a - 3*a + 6*a/*e |-- + ------------------------- for And(a > -oo, a < oo, a != 0) < 4 4 |a a | \ 1/4 otherwise
$$\begin{cases} \frac{\left(a^{3} - 3 a^{2} + 6 a - 6\right) e^{a}}{a^{4}} + \frac{6}{a^{4}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\frac{1}{4} & \text{otherwise} \end{cases}$$
Piecewise((6/a^4 + (-6 + a^3 - 3*a^2 + 6*a)*exp(a)/a^4, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (1/4, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.