Sr Examen
Integral de 1/(2+exp(x))^1/2 dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | ________ | / x | \/ 2 + e | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{e^{x} + 2}}\, dx$$
Integral(1/(sqrt(2 + exp(x))), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ | \/ 2 | |
||-\/ 2 *acoth|-----------| |
|| | ________| |
|| | / x | |
|| \\/ 2 + e / 1 |
/ ||-------------------------- for ------ > 1/2|
| || 2 x |
| 1 || 2 + e |
| ----------- dx = C + 2*|< |
| ________ || / ___ \ |
| / x || ___ | \/ 2 | |
| \/ 2 + e ||-\/ 2 *atanh|-----------| |
| || | ________| |
/ || | / x | |
|| \\/ 2 + e / 1 |
||-------------------------- for ------ < 1/2|
|| 2 x |
\\ 2 + e /
$$\int \frac{1}{\sqrt{e^{x} + 2}}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2}}{\sqrt{e^{x} + 2}} \right)}}{2} & \text{for}\: \frac{1}{e^{x} + 2} > \frac{1}{2} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{\sqrt{e^{x} + 2}} \right)}}{2} & \text{for}\: \frac{1}{e^{x} + 2} < \frac{1}{2} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ___\ / ___ \
___ |\/ 6 | ___ | \/ 2 |
\/ 2 *atanh|-----| - \/ 2 *atanh|---------|
\ 3 / | _______|
\\/ 2 + E /
$$- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{\sqrt{2 + e}} \right)} + \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{6}}{3} \right)}$$
=
=
/ ___\ / ___ \
___ |\/ 6 | ___ | \/ 2 |
\/ 2 *atanh|-----| - \/ 2 *atanh|---------|
\ 3 / | _______|
\\/ 2 + E /
$$- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{\sqrt{2 + e}} \right)} + \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{6}}{3} \right)}$$
sqrt(2)*atanh(sqrt(6)/3) - sqrt(2)*atanh(sqrt(2)/sqrt(2 + E))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.