Sr Examen
Integral de √(x+2)/x dx
Solución
Ha introducido
[src]
7 / | | _______ | \/ x + 2 | --------- dx | x | / 2
$$\int\limits_{2}^{7} \frac{\sqrt{x + 2}}{x}\, dx$$
Integral(sqrt(x + 2)/x, (x, 2, 7))
Respuesta (Indefinida)
[src]
// / ___ _______\ \
|| ___ |\/ 2 *\/ 2 + x | |
/ ||-\/ 2 *acoth|---------------| |
| || \ 2 / |
| _______ ||------------------------------ for 2 + x > 2|
| \/ x + 2 _______ || 2 |
| --------- dx = C + 2*\/ 2 + x + 4*|< |
| x || / ___ _______\ |
| || ___ |\/ 2 *\/ 2 + x | |
/ ||-\/ 2 *atanh|---------------| |
|| \ 2 / |
||------------------------------ for 2 + x < 2|
\\ 2 /
$$\int \frac{\sqrt{x + 2}}{x}\, dx = C + 2 \sqrt{x + 2} + 4 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)}}{2} & \text{for}\: x + 2 > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)}}{2} & \text{for}\: x + 2 < 2 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ___\
___ |3*\/ 2 | ___ / ___\
2 - 2*\/ 2 *acoth|-------| + 2*\/ 2 *acoth\\/ 2 /
\ 2 /
$$- 2 \sqrt{2} \operatorname{acoth}{\left(\frac{3 \sqrt{2}}{2} \right)} + 2 + 2 \sqrt{2} \operatorname{acoth}{\left(\sqrt{2} \right)}$$
=
=
/ ___\
___ |3*\/ 2 | ___ / ___\
2 - 2*\/ 2 *acoth|-------| + 2*\/ 2 *acoth\\/ 2 /
\ 2 /
$$- 2 \sqrt{2} \operatorname{acoth}{\left(\frac{3 \sqrt{2}}{2} \right)} + 2 + 2 \sqrt{2} \operatorname{acoth}{\left(\sqrt{2} \right)}$$
2 - 2*sqrt(2)*acoth(3*sqrt(2)/2) + 2*sqrt(2)*acoth(sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.