Sr Examen
Integral de x^4*e^(a*x) dx
Solución
Ha introducido
[src]
x / | | 4 a*x | x *E dx | / 0
$$\int\limits_{0}^{x} e^{a x} x^{4}\, dx$$
Integral(x^4*E^(a*x), (x, 0, x))
Respuesta (Indefinida)
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/// 4 4 3 3 2 2\ a*x \
||\24 + a *x - 24*a*x - 4*a *x + 12*a *x /*e 5 |
/ ||----------------------------------------------- for a != 0|
| || 5 |
| 4 a*x || a |
| x *E dx = C + |< |
| || 5 |
/ || x |
|| -- otherwise |
|| 5 |
\\ /
$$\int e^{a x} x^{4}\, dx = C + \begin{cases} \frac{\left(a^{4} x^{4} - 4 a^{3} x^{3} + 12 a^{2} x^{2} - 24 a x + 24\right) e^{a x}}{a^{5}} & \text{for}\: a^{5} \neq 0 \\\frac{x^{5}}{5} & \text{otherwise} \end{cases}$$
Respuesta
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/ / 4 4 3 3 2 2\ a*x | 24 \24 + a *x - 24*a*x - 4*a *x + 12*a *x /*e |- -- + ----------------------------------------------- for And(a > -oo, a < oo, a != 0) | 5 5 | a a < | 5 | x | -- otherwise | 5 \
$$\begin{cases} \frac{\left(a^{4} x^{4} - 4 a^{3} x^{3} + 12 a^{2} x^{2} - 24 a x + 24\right) e^{a x}}{a^{5}} - \frac{24}{a^{5}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\frac{x^{5}}{5} & \text{otherwise} \end{cases}$$
=
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/ / 4 4 3 3 2 2\ a*x | 24 \24 + a *x - 24*a*x - 4*a *x + 12*a *x /*e |- -- + ----------------------------------------------- for And(a > -oo, a < oo, a != 0) | 5 5 | a a < | 5 | x | -- otherwise | 5 \
$$\begin{cases} \frac{\left(a^{4} x^{4} - 4 a^{3} x^{3} + 12 a^{2} x^{2} - 24 a x + 24\right) e^{a x}}{a^{5}} - \frac{24}{a^{5}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\frac{x^{5}}{5} & \text{otherwise} \end{cases}$$
Piecewise((-24/a^5 + (24 + a^4*x^4 - 24*a*x - 4*a^3*x^3 + 12*a^2*x^2)*exp(a*x)/a^5, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (x^5/5, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.