Sr Examen
Integral de e^x/(e^(2*x)+5) dx
Solución
Ha introducido
[src]
1 / | | x | E | -------- dx | 2*x | E + 5 | / 0
$$\int\limits_{0}^{1} \frac{e^{x}}{e^{2 x} + 5}\, dx$$
Integral(E^x/(E^(2*x) + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ x\ | ___ |\/ 5 *e | | x \/ 5 *atan|--------| | E \ 5 / | -------- dx = C + -------------------- | 2*x 5 | E + 5 | /
$$\int \frac{e^{x}}{e^{2 x} + 5}\, dx = C + \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} e^{x}}{5} \right)}}{5}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \ - RootSum\20*z + 1, i -> i*log(1 + 10*i)/ + RootSum\20*z + 1, i -> i*log(E + 10*i)/
$$- \operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + e \right)} \right)\right)}$$
=
=
/ 2 \ / 2 \ - RootSum\20*z + 1, i -> i*log(1 + 10*i)/ + RootSum\20*z + 1, i -> i*log(E + 10*i)/
$$- \operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + e \right)} \right)\right)}$$
-RootSum(20*_z^2 + 1, Lambda(_i, _i*log(1 + 10*_i))) + RootSum(20*_z^2 + 1, Lambda(_i, _i*log(E + 10*_i)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.