Sr Examen
Integral de (1+cos(2*x))/(1-(1+cos(2*x))/2*k)^(1/2) dx
Solución
Ha introducido
[src]
1 / | | 1 + cos(2*x) | ------------------------ dx | ____________________ | / 1 + cos(2*x) | / 1 - ------------*k | \/ 2 | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(2 x \right)} + 1}{\sqrt{- k \frac{\cos{\left(2 x \right)} + 1}{2} + 1}}\, dx$$
Integral((1 + cos(2*x))/sqrt(1 - (1 + cos(2*x))/2*k), (x, 0, 1))
Respuesta
[src]
/ 1 1 \
| / / |
| | | |
___ | | 1 | cos(2*x) |
\/ 2 *| | ---------------------- dx + | ---------------------- dx|
| | ____________________ | ____________________ |
| | \/ 2 - k - k*cos(2*x) | \/ 2 - k - k*cos(2*x) |
| | | |
|/ / |
\0 0 /
$$\sqrt{2} \left(\int\limits_{0}^{1} \frac{\cos{\left(2 x \right)}}{\sqrt{- k \cos{\left(2 x \right)} - k + 2}}\, dx + \int\limits_{0}^{1} \frac{1}{\sqrt{- k \cos{\left(2 x \right)} - k + 2}}\, dx\right)$$
=
=
/ 1 1 \
| / / |
| | | |
___ | | 1 | cos(2*x) |
\/ 2 *| | ---------------------- dx + | ---------------------- dx|
| | ____________________ | ____________________ |
| | \/ 2 - k - k*cos(2*x) | \/ 2 - k - k*cos(2*x) |
| | | |
|/ / |
\0 0 /
$$\sqrt{2} \left(\int\limits_{0}^{1} \frac{\cos{\left(2 x \right)}}{\sqrt{- k \cos{\left(2 x \right)} - k + 2}}\, dx + \int\limits_{0}^{1} \frac{1}{\sqrt{- k \cos{\left(2 x \right)} - k + 2}}\, dx\right)$$
sqrt(2)*(Integral(1/sqrt(2 - k - k*cos(2*x)), (x, 0, 1)) + Integral(cos(2*x)/sqrt(2 - k - k*cos(2*x)), (x, 0, 1)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.