Sr Examen
Integral de sin(2*m*x)/e^(a*x) dx
Solución
Ha introducido
[src]
1 / | | sin(2*m*x) | ---------- dx | a*x | E | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(2 m x \right)}}{e^{a x}}\, dx$$
Integral(sin((2*m)*x)/E^(a*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / | | | sin(2*m*x) | -a*x | ---------- dx = C + | e *sin(2*m*x) dx | a*x | | E / | /
$$\int \frac{\sin{\left(2 m x \right)}}{e^{a x}}\, dx = C + \int e^{- a x} \sin{\left(2 m x \right)}\, dx$$
Respuesta
[src]
/ 0 for Or(And(a = 0, m = 0), And(a = 0, a = -2*I*m, m = 0), And(a = 0, a = 2*I*m, m = 0), And(a = 0, a = -2*I*m, a = 2*I*m, m = 0)) | | 2*I*m 2*I*m 2*I*m | e *sin(2*m) I*cos(2*m)*e I*e *sin(2*m) | --------------- + ----------------- - ----------------- for Or(And(a = 0, a = -2*I*m), And(a = -2*I*m, a = 2*I*m), And(a = -2*I*m, m = 0), And(a = 0, a = -2*I*m, a = 2*I*m), And(a = -2*I*m, a = 2*I*m, m = 0), a = -2*I*m) | 2 2 4*m | | -2*I*m -2*I*m -2*I*m
$$\begin{cases} 0 & \text{for}\: \left(a = 0 \wedge m = 0\right) \vee \left(a = 0 \wedge a = - 2 i m \wedge m = 0\right) \vee \left(a = 0 \wedge a = 2 i m \wedge m = 0\right) \vee \left(a = 0 \wedge a = - 2 i m \wedge a = 2 i m \wedge m = 0\right) \\\frac{e^{2 i m} \sin{\left(2 m \right)}}{2} + \frac{i e^{2 i m} \cos{\left(2 m \right)}}{2} - \frac{i e^{2 i m} \sin{\left(2 m \right)}}{4 m} & \text{for}\: \left(a = 0 \wedge a = - 2 i m\right) \vee \left(a = - 2 i m \wedge a = 2 i m\right) \vee \left(a = - 2 i m \wedge m = 0\right) \vee \left(a = 0 \wedge a = - 2 i m \wedge a = 2 i m\right) \vee \left(a = - 2 i m \wedge a = 2 i m \wedge m = 0\right) \vee a = - 2 i m \\\frac{e^{- 2 i m} \sin{\left(2 m \right)}}{2} - \frac{i e^{- 2 i m} \cos{\left(2 m \right)}}{2} + \frac{i e^{- 2 i m} \sin{\left(2 m \right)}}{4 m} & \text{for}\: \left(a = 0 \wedge a = 2 i m\right) \vee \left(a = 2 i m \wedge m = 0\right) \vee a = 2 i m \\- \frac{a \sin{\left(2 m \right)}}{a^{2} e^{a} + 4 m^{2} e^{a}} - \frac{2 m \cos{\left(2 m \right)}}{a^{2} e^{a} + 4 m^{2} e^{a}} + \frac{2 m}{a^{2} + 4 m^{2}} & \text{otherwise} \end{cases}$$
=
=
/ 0 for Or(And(a = 0, m = 0), And(a = 0, a = -2*I*m, m = 0), And(a = 0, a = 2*I*m, m = 0), And(a = 0, a = -2*I*m, a = 2*I*m, m = 0)) | | 2*I*m 2*I*m 2*I*m | e *sin(2*m) I*cos(2*m)*e I*e *sin(2*m) | --------------- + ----------------- - ----------------- for Or(And(a = 0, a = -2*I*m), And(a = -2*I*m, a = 2*I*m), And(a = -2*I*m, m = 0), And(a = 0, a = -2*I*m, a = 2*I*m), And(a = -2*I*m, a = 2*I*m, m = 0), a = -2*I*m) | 2 2 4*m | | -2*I*m -2*I*m -2*I*m
$$\begin{cases} 0 & \text{for}\: \left(a = 0 \wedge m = 0\right) \vee \left(a = 0 \wedge a = - 2 i m \wedge m = 0\right) \vee \left(a = 0 \wedge a = 2 i m \wedge m = 0\right) \vee \left(a = 0 \wedge a = - 2 i m \wedge a = 2 i m \wedge m = 0\right) \\\frac{e^{2 i m} \sin{\left(2 m \right)}}{2} + \frac{i e^{2 i m} \cos{\left(2 m \right)}}{2} - \frac{i e^{2 i m} \sin{\left(2 m \right)}}{4 m} & \text{for}\: \left(a = 0 \wedge a = - 2 i m\right) \vee \left(a = - 2 i m \wedge a = 2 i m\right) \vee \left(a = - 2 i m \wedge m = 0\right) \vee \left(a = 0 \wedge a = - 2 i m \wedge a = 2 i m\right) \vee \left(a = - 2 i m \wedge a = 2 i m \wedge m = 0\right) \vee a = - 2 i m \\\frac{e^{- 2 i m} \sin{\left(2 m \right)}}{2} - \frac{i e^{- 2 i m} \cos{\left(2 m \right)}}{2} + \frac{i e^{- 2 i m} \sin{\left(2 m \right)}}{4 m} & \text{for}\: \left(a = 0 \wedge a = 2 i m\right) \vee \left(a = 2 i m \wedge m = 0\right) \vee a = 2 i m \\- \frac{a \sin{\left(2 m \right)}}{a^{2} e^{a} + 4 m^{2} e^{a}} - \frac{2 m \cos{\left(2 m \right)}}{a^{2} e^{a} + 4 m^{2} e^{a}} + \frac{2 m}{a^{2} + 4 m^{2}} & \text{otherwise} \end{cases}$$
Piecewise((0, ((a = 0)∧(m = 0))∨((a = 0)∧(m = 0)∧(a = -2*i*m))∨((a = 0)∧(m = 0)∧(a = 2*i*m))∨((a = 0)∧(m = 0)∧(a = -2*i*m)∧(a = 2*i*m))), (exp(2*i*m)*sin(2*m)/2 + i*cos(2*m)*exp(2*i*m)/2 - i*exp(2*i*m)*sin(2*m)/(4*m), (a = -2*i*m)∨((a = 0)∧(a = -2*i*m))∨((m = 0)∧(a = -2*i*m))∨((a = -2*i*m)∧(a = 2*i*m))∨((a = 0)∧(a = -2*i*m)∧(a = 2*i*m))∨((m = 0)∧(a = -2*i*m)∧(a = 2*i*m))), (exp(-2*i*m)*sin(2*m)/2 - i*cos(2*m)*exp(-2*i*m)/2 + i*exp(-2*i*m)*sin(2*m)/(4*m), (a = 2*i*m)∨((a = 0)∧(a = 2*i*m))∨((m = 0)∧(a = 2*i*m))), (2*m/(a^2 + 4*m^2) - a*sin(2*m)/(a^2*exp(a) + 4*m^2*exp(a)) - 2*m*cos(2*m)/(a^2*exp(a) + 4*m^2*exp(a)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.