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