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