Integral de cos(ax+b) dx
Solución
Respuesta (Indefinida)
[src]
/ //sin(a*x + b) \
| ||------------ for a != 0|
| cos(a*x + b) dx = C + |< a |
| || |
/ \\ sin(b) otherwise /
$$\int \cos{\left(a x + b \right)}\, dx = C + \begin{cases} \frac{\sin{\left(a x + b \right)}}{a} & \text{for}\: a \neq 0 \\\sin{\left(b \right)} & \text{otherwise} \end{cases}$$
/sin(a + b) sin(b)
|---------- - ------ for And(a > -oo, a < oo, a != 0)
< a a
|
\ cos(b) otherwise
$$\begin{cases} - \frac{\sin{\left(b \right)}}{a} + \frac{\sin{\left(a + b \right)}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}$$
=
/sin(a + b) sin(b)
|---------- - ------ for And(a > -oo, a < oo, a != 0)
< a a
|
\ cos(b) otherwise
$$\begin{cases} - \frac{\sin{\left(b \right)}}{a} + \frac{\sin{\left(a + b \right)}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}$$
Piecewise((sin(a + b)/a - sin(b)/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (cos(b), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.