Sr Examen
Integral de (e^(3x))/(5e^(5*x)+1) dx
Solución
Ha introducido
[src]
1 / | | 3*x | E | ---------- dx | 5*x | 5*E + 1 | / 0
$$\int\limits_{0}^{1} \frac{e^{3 x}}{5 e^{5 x} + 1}\, dx$$
Integral(E^(3*x)/(5*E^(5*x) + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 3*x | E / 5 / 2 x\\ | ---------- dx = C + RootSum\390625*z - 1, i -> i*log\125*i + e // | 5*x | 5*E + 1 | /
$$\int \frac{e^{3 x}}{5 e^{5 x} + 1}\, dx = C + \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + e^{x} \right)} \right)\right)}$$
Gráfica
Respuesta
[src]
/ 5 / 2\\ / 5 / 2\\ - RootSum\390625*z - 1, i -> i*log\1 + 125*i // + RootSum\390625*z - 1, i -> i*log\E + 125*i //
$$- \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + e \right)} \right)\right)}$$
=
=
/ 5 / 2\\ / 5 / 2\\ - RootSum\390625*z - 1, i -> i*log\1 + 125*i // + RootSum\390625*z - 1, i -> i*log\E + 125*i //
$$- \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + e \right)} \right)\right)}$$
-RootSum(390625*_z^5 - 1, Lambda(_i, _i*log(1 + 125*_i^2))) + RootSum(390625*_z^5 - 1, Lambda(_i, _i*log(E + 125*_i^2)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.