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