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