Sr Examen
Integral de sqrt(x+6)/(x-2) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ x + 6 | --------- dx | x - 2 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 6}}{x - 2}\, dx$$
Integral(sqrt(x + 6)/(x - 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ _______\ \
|| ___ |\/ 2 *\/ 6 + x | |
/ ||-\/ 2 *acoth|---------------| |
| || \ 4 / |
| _______ ||------------------------------ for 6 + x > 8|
| \/ x + 6 _______ || 4 |
| --------- dx = C + 2*\/ 6 + x + 16*|< |
| x - 2 || / ___ _______\ |
| || ___ |\/ 2 *\/ 6 + x | |
/ ||-\/ 2 *atanh|---------------| |
|| \ 4 / |
||------------------------------ for 6 + x < 8|
\\ 4 /
$$\int \frac{\sqrt{x + 6}}{x - 2}\, dx = C + 2 \sqrt{x + 6} + 16 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \sqrt{x + 6}}{4} \right)}}{4} & \text{for}\: x + 6 > 8 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \sqrt{x + 6}}{4} \right)}}{4} & \text{for}\: x + 6 < 8 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ____\ / ___\
___ ___ ___ |\/ 14 | ___ |\/ 3 |
- 2*\/ 6 + 2*\/ 7 - 4*\/ 2 *atanh|------| + 4*\/ 2 *atanh|-----|
\ 4 / \ 2 /
$$- 4 \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{14}}{4} \right)} - 2 \sqrt{6} + 2 \sqrt{7} + 4 \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{3}}{2} \right)}$$
=
=
/ ____\ / ___\
___ ___ ___ |\/ 14 | ___ |\/ 3 |
- 2*\/ 6 + 2*\/ 7 - 4*\/ 2 *atanh|------| + 4*\/ 2 *atanh|-----|
\ 4 / \ 2 /
$$- 4 \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{14}}{4} \right)} - 2 \sqrt{6} + 2 \sqrt{7} + 4 \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{3}}{2} \right)}$$
-2*sqrt(6) + 2*sqrt(7) - 4*sqrt(2)*atanh(sqrt(14)/4) + 4*sqrt(2)*atanh(sqrt(3)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.