Sr Examen
Integral de sqrt(1x+6)/x dx
Solución
Ha introducido
[src]
2 / | | _______ | \/ x + 6 | --------- dx | x | / 1
$$\int\limits_{1}^{2} \frac{\sqrt{x + 6}}{x}\, dx$$
Integral(sqrt(x + 6)/x, (x, 1, 2))
Respuesta (Indefinida)
[src]
// / ___ _______\ \
|| ___ |\/ 6 *\/ 6 + x | |
/ ||-\/ 6 *acoth|---------------| |
| || \ 6 / |
| _______ ||------------------------------ for 6 + x > 6|
| \/ x + 6 _______ || 6 |
| --------- dx = C + 2*\/ 6 + x + 12*|< |
| x || / ___ _______\ |
| || ___ |\/ 6 *\/ 6 + x | |
/ ||-\/ 6 *atanh|---------------| |
|| \ 6 / |
||------------------------------ for 6 + x < 6|
\\ 6 /
$$\int \frac{\sqrt{x + 6}}{x}\, dx = C + 2 \sqrt{x + 6} + 12 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \sqrt{x + 6}}{6} \right)}}{6} & \text{for}\: x + 6 > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \sqrt{x + 6}}{6} \right)}}{6} & \text{for}\: x + 6 < 6 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ___\ / ____\
___ ___ ___ |2*\/ 3 | ___ |\/ 42 |
- 2*\/ 7 + 4*\/ 2 - 2*\/ 6 *acoth|-------| + 2*\/ 6 *acoth|------|
\ 3 / \ 6 /
$$- 2 \sqrt{6} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)} - 2 \sqrt{7} + 4 \sqrt{2} + 2 \sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{42}}{6} \right)}$$
=
=
/ ___\ / ____\
___ ___ ___ |2*\/ 3 | ___ |\/ 42 |
- 2*\/ 7 + 4*\/ 2 - 2*\/ 6 *acoth|-------| + 2*\/ 6 *acoth|------|
\ 3 / \ 6 /
$$- 2 \sqrt{6} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)} - 2 \sqrt{7} + 4 \sqrt{2} + 2 \sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{42}}{6} \right)}$$
-2*sqrt(7) + 4*sqrt(2) - 2*sqrt(6)*acoth(2*sqrt(3)/3) + 2*sqrt(6)*acoth(sqrt(42)/6)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.