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