Sr Examen
Integral de (2*exp^(2*x)*(2+3*cos(x)))/(1-(cos(x))^2) dx
Solución
Ha introducido
[src]
1 / | | 2*x | 2*E *(2 + 3*cos(x)) | --------------------- dx | 2 | 1 - cos (x) | / 0
$$\int\limits_{0}^{1} \frac{2 e^{2 x} \left(3 \cos{\left(x \right)} + 2\right)}{1 - \cos^{2}{\left(x \right)}}\, dx$$
Integral(((2*E^(2*x))*(2 + 3*cos(x)))/(1 - cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / / | | | | 2*x | 2*x | 2*x | 2*E *(2 + 3*cos(x)) | cos(x)*e | e | --------------------- dx = C - 6* | -------------------------- dx - 4* | -------------------------- dx | 2 | (1 + cos(x))*(-1 + cos(x)) | (1 + cos(x))*(-1 + cos(x)) | 1 - cos (x) | | | / / /
$$\int \frac{2 e^{2 x} \left(3 \cos{\left(x \right)} + 2\right)}{1 - \cos^{2}{\left(x \right)}}\, dx = C - 4 \int \frac{e^{2 x}}{\left(\cos{\left(x \right)} - 1\right) \left(\cos{\left(x \right)} + 1\right)}\, dx - 6 \int \frac{e^{2 x} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right) \left(\cos{\left(x \right)} + 1\right)}\, dx$$
Respuesta
[src]
1 1
/ /
| |
| 2*x | 2*x
| 2*e | 3*cos(x)*e
- 2* | ------------ dx - 2* | ------------- dx
| 2 | 2
| -1 + cos (x) | -1 + cos (x)
| |
/ /
0 0
$$- 2 \int\limits_{0}^{1} \frac{2 e^{2 x}}{\cos^{2}{\left(x \right)} - 1}\, dx - 2 \int\limits_{0}^{1} \frac{3 e^{2 x} \cos{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}\, dx$$
=
=
1 1
/ /
| |
| 2*x | 2*x
| 2*e | 3*cos(x)*e
- 2* | ------------ dx - 2* | ------------- dx
| 2 | 2
| -1 + cos (x) | -1 + cos (x)
| |
/ /
0 0
$$- 2 \int\limits_{0}^{1} \frac{2 e^{2 x}}{\cos^{2}{\left(x \right)} - 1}\, dx - 2 \int\limits_{0}^{1} \frac{3 e^{2 x} \cos{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}\, dx$$
-2*Integral(2*exp(2*x)/(-1 + cos(x)^2), (x, 0, 1)) - 2*Integral(3*cos(x)*exp(2*x)/(-1 + cos(x)^2), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.