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