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