Sr Examen
Integral de 1/(5*e^x+2*e^-x) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | x -x | 5*E + 2*E | / 0
$$\int\limits_{0}^{1} \frac{1}{5 e^{x} + 2 e^{- x}}\, dx$$
Integral(1/(5*E^x + 2*E^(-x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ____ x\ / ____ |\/ 10 *e | | \/ 10 *atan|---------| | 1 \ 2 / | ------------ dx = C + ---------------------- | x -x 10 | 5*E + 2*E | /
$$\int \frac{1}{5 e^{x} + 2 e^{- x}}\, dx = C + \frac{\sqrt{10} \operatorname{atan}{\left(\frac{\sqrt{10} e^{x}}{2} \right)}}{10}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \ - RootSum\40*z + 1, i -> i*log(1 + 4*i)/ + RootSum\40*z + 1, i -> i*log(E + 4*i)/
$$- \operatorname{RootSum} {\left(40 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(40 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + e \right)} \right)\right)}$$
=
=
/ 2 \ / 2 \ - RootSum\40*z + 1, i -> i*log(1 + 4*i)/ + RootSum\40*z + 1, i -> i*log(E + 4*i)/
$$- \operatorname{RootSum} {\left(40 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(40 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + e \right)} \right)\right)}$$
-RootSum(40*_z^2 + 1, Lambda(_i, _i*log(1 + 4*_i))) + RootSum(40*_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.