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