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