Sr Examen
Integral de cosh(3*t)*e^(t*(-s)) dx
Solución
Ha introducido
[src]
1 / | | t*(-s) | cosh(3*t)*E dt | / 0
$$\int\limits_{0}^{1} e^{- s t} \cosh{\left(3 t \right)}\, dt$$
Integral(cosh(3*t)*E^(t*(-s)), (t, 0, 1))
Respuesta (Indefinida)
[src]
// 3*t 3*t 3*t \
|| cosh(3*t)*e t*cosh(3*t)*e t*e *sinh(3*t) |
|| -------------- + ---------------- - ---------------- for s = -3|
|| 6 2 2 |
/ || |
| || -3*t -3*t -3*t |
| t*(-s) || cosh(3*t)*e t*cosh(3*t)*e t*e *sinh(3*t) |
| cosh(3*t)*E dt = C + |<- --------------- + ----------------- + ----------------- for s = 3 |
| || 6 2 2 |
/ || |
|| 3*sinh(3*t) s*cosh(3*t) |
|| - ------------------ - ------------------ otherwise |
|| s*t 2 s*t s*t 2 s*t |
|| - 9*e + s *e - 9*e + s *e |
\\ /
$$\int e^{- s t} \cosh{\left(3 t \right)}\, dt = C + \begin{cases} - \frac{t e^{3 t} \sinh{\left(3 t \right)}}{2} + \frac{t e^{3 t} \cosh{\left(3 t \right)}}{2} + \frac{e^{3 t} \cosh{\left(3 t \right)}}{6} & \text{for}\: s = -3 \\\frac{t e^{- 3 t} \sinh{\left(3 t \right)}}{2} + \frac{t e^{- 3 t} \cosh{\left(3 t \right)}}{2} - \frac{e^{- 3 t} \cosh{\left(3 t \right)}}{6} & \text{for}\: s = 3 \\- \frac{s \cosh{\left(3 t \right)}}{s^{2} e^{s t} - 9 e^{s t}} - \frac{3 \sinh{\left(3 t \right)}}{s^{2} e^{s t} - 9 e^{s t}} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ 3 3 | cosh(3)*e e *sinh(3) | ---------- - ---------- for s = -3 | 2 3 | | -3 -3 | cosh(3)*e 2*e *sinh(3) < ----------- + ------------- for s = 3 | 2 3 | | s 3*sinh(3) s*cosh(3) |------- - -------------- - -------------- otherwise | 2 s 2 s s 2 s |-9 + s - 9*e + s *e - 9*e + s *e \
$$\begin{cases} - \frac{e^{3} \sinh{\left(3 \right)}}{3} + \frac{e^{3} \cosh{\left(3 \right)}}{2} & \text{for}\: s = -3 \\\frac{\cosh{\left(3 \right)}}{2 e^{3}} + \frac{2 \sinh{\left(3 \right)}}{3 e^{3}} & \text{for}\: s = 3 \\- \frac{s \cosh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} + \frac{s}{s^{2} - 9} - \frac{3 \sinh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} & \text{otherwise} \end{cases}$$
=
=
/ 3 3 | cosh(3)*e e *sinh(3) | ---------- - ---------- for s = -3 | 2 3 | | -3 -3 | cosh(3)*e 2*e *sinh(3) < ----------- + ------------- for s = 3 | 2 3 | | s 3*sinh(3) s*cosh(3) |------- - -------------- - -------------- otherwise | 2 s 2 s s 2 s |-9 + s - 9*e + s *e - 9*e + s *e \
$$\begin{cases} - \frac{e^{3} \sinh{\left(3 \right)}}{3} + \frac{e^{3} \cosh{\left(3 \right)}}{2} & \text{for}\: s = -3 \\\frac{\cosh{\left(3 \right)}}{2 e^{3}} + \frac{2 \sinh{\left(3 \right)}}{3 e^{3}} & \text{for}\: s = 3 \\- \frac{s \cosh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} + \frac{s}{s^{2} - 9} - \frac{3 \sinh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} & \text{otherwise} \end{cases}$$
Piecewise((cosh(3)*exp(3)/2 - exp(3)*sinh(3)/3, s = -3), (cosh(3)*exp(-3)/2 + 2*exp(-3)*sinh(3)/3, s = 3), (s/(-9 + s^2) - 3*sinh(3)/(-9*exp(s) + s^2*exp(s)) - s*cosh(3)/(-9*exp(s) + s^2*exp(s)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.