Sr Examen
Integral de a^3*sin(a*x)/(a^4+4) dx
Solución
Ha introducido
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oo / | | 3 | a *sin(a*x) | ----------- dx | 4 | a + 4 | / 0
$$\int\limits_{0}^{\infty} \frac{a^{3} \sin{\left(a x \right)}}{a^{4} + 4}\, dx$$
Integral((a^3*sin(a*x))/(a^4 + 4), (x, 0, oo))
Respuesta (Indefinida)
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// 0 for a = 0\ / 3 || | | a *|<-cos(a*x) | | 3 ||---------- otherwise| | a *sin(a*x) \\ a / | ----------- dx = C + --------------------------- | 4 4 | a + 4 a + 4 | /
$$\int \frac{a^{3} \sin{\left(a x \right)}}{a^{4} + 4}\, dx = C + \frac{a^{3} \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos{\left(a x \right)}}{a} & \text{otherwise} \end{cases}\right)}{a^{4} + 4}$$
Respuesta
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/ 2 2 | a a *cos(zoo*a) |------ - ------------- for And(a > -oo, a < oo, a != 0) < 4 4 |4 + a 4 + a | \ 0 otherwise
$$\begin{cases} - \frac{a^{2} \cos{\left(\tilde{\infty} a \right)}}{a^{4} + 4} + \frac{a^{2}}{a^{4} + 4} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/ 2 2 | a a *cos(zoo*a) |------ - ------------- for And(a > -oo, a < oo, a != 0) < 4 4 |4 + a 4 + a | \ 0 otherwise
$$\begin{cases} - \frac{a^{2} \cos{\left(\tilde{\infty} a \right)}}{a^{4} + 4} + \frac{a^{2}}{a^{4} + 4} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((a^2/(4 + a^4) - a^2*cos(±oo*a)/(4 + a^4), (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.