Sr Examen
Integral de 1/(e^(x/4)+4e^(-x/4)) dx
Solución
Ha introducido
[src]
4*log(2)
/
|
| 1
| ----------- dx
| x -x
| - ---
| 4 4
| E + 4*E
|
/
/ 2 \
4*log|-----|
|3 ___|
\\/ x /
$$\int\limits_{4 \log{\left(\frac{2}{\sqrt[3]{x}} \right)}}^{4 \log{\left(2 \right)}} \frac{1}{4 e^{\frac{\left(-1\right) x}{4}} + e^{\frac{x}{4}}}\, dx$$
Integral(1/(E^(x/4) + 4*E^((-x)/4)), (x, 4*log(2/x^(1/3)), 4*log(2)))
Respuesta (Indefinida)
[src]
/ x\ / | -| | | 4| | 1 |e | | ----------- dx = C + 2*atan|--| | x -x \2 / | - --- | 4 4 | E + 4*E | /
$$\int \frac{1}{4 e^{\frac{\left(-1\right) x}{4}} + e^{\frac{x}{4}}}\, dx = C + 2 \operatorname{atan}{\left(\frac{e^{\frac{x}{4}}}{2} \right)}$$
Respuesta
[src]
/ 2 / 2 \\ / 2 \
- RootSum|z + 1, i -> i*log|----- + 2*i|| + RootSum\z + 1, i -> i*log(2 + 2*i)/
| |3 ___ ||
\ \\/ x //
$$\operatorname{RootSum} {\left(z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 2 \right)} \right)\right)} - \operatorname{RootSum} {\left(z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \frac{2}{\sqrt[3]{x}} \right)} \right)\right)}$$
=
=
/ 2 / 2 \\ / 2 \
- RootSum|z + 1, i -> i*log|----- + 2*i|| + RootSum\z + 1, i -> i*log(2 + 2*i)/
| |3 ___ ||
\ \\/ x //
$$\operatorname{RootSum} {\left(z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 2 \right)} \right)\right)} - \operatorname{RootSum} {\left(z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \frac{2}{\sqrt[3]{x}} \right)} \right)\right)}$$
-RootSum(_z^2 + 1, Lambda(_i, _i*log(2/x^(1/3) + 2*_i))) + RootSum(_z^2 + 1, Lambda(_i, _i*log(2 + 2*_i)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.