Integral de (cos(ax)+sin(ax))^2 dx
Solución
Respuesta (Indefinida)
[src]
/ // 0 for a = 0\
| || |
| 2 || 2 |
| (cos(a*x) + sin(a*x)) dx = C + x + 2*|<-cos (a*x) |
| ||----------- otherwise|
/ || 2*a |
\\ /
$$\int \left(\sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}\, dx = C + x + 2 \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos^{2}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)$$
/ 2
|1 2 2 cos (a)
|- + cos (a) + sin (a) - ------- for And(a > -oo, a < oo, a != 0)
$$\begin{cases} \sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)} - \frac{\cos^{2}{\left(a \right)}}{a} + \frac{1}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\1 & \text{otherwise} \end{cases}$$
=
/ 2
|1 2 2 cos (a)
|- + cos (a) + sin (a) - ------- for And(a > -oo, a < oo, a != 0)
$$\begin{cases} \sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)} - \frac{\cos^{2}{\left(a \right)}}{a} + \frac{1}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\1 & \text{otherwise} \end{cases}$$
Piecewise((1/a + cos(a)^2 + sin(a)^2 - cos(a)^2/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (1, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.