Sr Examen
Integral de e^x/(2-e^(2*x)) dx
Solución
Ha introducido
[src]
1 / | | x | E | -------- dx | 2*x | 2 - E | / 0
$$\int\limits_{0}^{1} \frac{e^{x}}{2 - e^{2 x}}\, dx$$
Integral(E^x/(2 - E^(2*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ x\ \
|| ___ |\/ 2 *e | |
/ ||-\/ 2 *acoth|--------| |
| || \ 2 / 2*x |
| x ||----------------------- for e > 2|
| E || 2 |
| -------- dx = C - |< |
| 2*x || / ___ x\ |
| 2 - E || ___ |\/ 2 *e | |
| ||-\/ 2 *atanh|--------| |
/ || \ 2 / 2*x |
||----------------------- for e < 2|
\\ 2 /
$$\int \frac{e^{x}}{2 - e^{2 x}}\, dx = C - \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} e^{x}}{2} \right)}}{2} & \text{for}\: e^{2 x} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} e^{x}}{2} \right)}}{2} & \text{for}\: e^{2 x} < 2 \end{cases}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \ - RootSum\8*z - 1, i -> i*log(1 + 4*i)/ + RootSum\8*z - 1, i -> i*log(E + 4*i)/
$$- \operatorname{RootSum} {\left(8 z^{2} - 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{2} - 1, \left( i \mapsto i \log{\left(4 i + e \right)} \right)\right)}$$
=
=
/ 2 \ / 2 \ - RootSum\8*z - 1, i -> i*log(1 + 4*i)/ + RootSum\8*z - 1, i -> i*log(E + 4*i)/
$$- \operatorname{RootSum} {\left(8 z^{2} - 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{2} - 1, \left( i \mapsto i \log{\left(4 i + e \right)} \right)\right)}$$
-RootSum(8*_z^2 - 1, Lambda(_i, _i*log(1 + 4*_i))) + RootSum(8*_z^2 - 1, Lambda(_i, _i*log(E + 4*_i)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.