Sr Examen
Integral de (cosax)/(sin⁵ax) dx
Solución
Ha introducido
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1 / | | cos(a*x) | --------- dx | 5 | sin (a*x) | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(a x \right)}}{\sin^{5}{\left(a x \right)}}\, dx$$
Integral(cos(a*x)/sin(a*x)^5, (x, 0, 1))
Respuesta (Indefinida)
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/ // -1 \ | ||------------- for a != 0| | cos(a*x) || 4 | | --------- dx = C + |<4*a*sin (a*x) | | 5 || | | sin (a*x) || zoo*x otherwise | | \\ / /
$$\int \frac{\cos{\left(a x \right)}}{\sin^{5}{\left(a x \right)}}\, dx = C + \begin{cases} - \frac{1}{4 a \sin^{4}{\left(a x \right)}} & \text{for}\: a \neq 0 \\\tilde{\infty} x & \text{otherwise} \end{cases}$$
Respuesta
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/ /1 \ 1 |oo*sign|--| - ----------- for And(a > -oo, a < oo, a != 0) | | 5| 4 < \a / 4*a*sin (a) | | 0 otherwise \
$$\begin{cases} \infty \operatorname{sign}{\left(\frac{1}{a^{5}} \right)} - \frac{1}{4 a \sin^{4}{\left(a \right)}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/ /1 \ 1 |oo*sign|--| - ----------- for And(a > -oo, a < oo, a != 0) | | 5| 4 < \a / 4*a*sin (a) | | 0 otherwise \
$$\begin{cases} \infty \operatorname{sign}{\left(\frac{1}{a^{5}} \right)} - \frac{1}{4 a \sin^{4}{\left(a \right)}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((oo*sign(a^(-5)) - 1/(4*a*sin(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.