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