Sr Examen
Integral de 15a(tan^3at*sec^3at)*dt dx
Solución
Ha introducido
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1 / | | 3 3 | 15*a*tan (a*t)*sec (a*t) dt | / 0
$$\int\limits_{0}^{1} 15 a \tan^{3}{\left(a t \right)} \sec^{3}{\left(a t \right)}\, dt$$
Integral((15*a)*(tan(a*t)^3*sec(a*t)^3), (t, 0, 1))
Respuesta (Indefinida)
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// 0 for a = 0\
/ || |
| || 3 5 |
| 3 3 || sec (a*t) sec (a*t) |
| 15*a*tan (a*t)*sec (a*t) dt = C + 15*a*|<- --------- + --------- |
| || 3 5 |
/ ||----------------------- otherwise|
|| a |
\\ /
$$\int 15 a \tan^{3}{\left(a t \right)} \sec^{3}{\left(a t \right)}\, dt = C + 15 a \left(\begin{cases} 0 & \text{for}\: a = 0 \\\frac{\frac{\sec^{5}{\left(a t \right)}}{5} - \frac{\sec^{3}{\left(a t \right)}}{3}}{a} & \text{otherwise} \end{cases}\right)$$
Respuesta
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/ 2 | -3 + 5*cos (a) |2 - -------------- for And(a > -oo, a < oo, a != 0) < 5 | cos (a) | \ 0 otherwise
$$\begin{cases} - \frac{5 \cos^{2}{\left(a \right)} - 3}{\cos^{5}{\left(a \right)}} + 2 & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ 2 | -3 + 5*cos (a) |2 - -------------- for And(a > -oo, a < oo, a != 0) < 5 | cos (a) | \ 0 otherwise
$$\begin{cases} - \frac{5 \cos^{2}{\left(a \right)} - 3}{\cos^{5}{\left(a \right)}} + 2 & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((2 - (-3 + 5*cos(a)^2)/cos(a)^5, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.