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