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