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