Sr Examen
Integral de 1/((x-1)sqrt(x+6)) dx
Solución
Ha introducido
[src]
10 / | | 1 | ----------------- dx | _______ | (x - 1)*\/ x + 6 | / 3
$$\int\limits_{3}^{10} \frac{1}{\left(x - 1\right) \sqrt{x + 6}}\, dx$$
Integral(1/((x - 1)*sqrt(x + 6)), (x, 3, 10))
Respuesta (Indefinida)
[src]
// / ___ _______\ \
|| ___ |\/ 7 *\/ 6 + x | |
||-\/ 7 *acoth|---------------| |
/ || \ 7 / |
| ||------------------------------ for 6 + x > 7|
| 1 || 7 |
| ----------------- dx = C + 2*|< |
| _______ || / ___ _______\ |
| (x - 1)*\/ x + 6 || ___ |\/ 7 *\/ 6 + x | |
| ||-\/ 7 *atanh|---------------| |
/ || \ 7 / |
||------------------------------ for 6 + x < 7|
\\ 7 /
$$\int \frac{1}{\left(x - 1\right) \sqrt{x + 6}}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{\sqrt{7} \sqrt{x + 6}}{7} \right)}}{7} & \text{for}\: x + 6 > 7 \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7} \sqrt{x + 6}}{7} \right)}}{7} & \text{for}\: x + 6 < 7 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |\/ 7 | ___ |\/ 7 |
2*\/ 7 *atanh|-----| 2*\/ 7 *atanh|-----|
\ 4 / \ 3 /
- -------------------- + --------------------
7 7
$$- \frac{2 \sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7}}{4} \right)}}{7} + \frac{2 \sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7}}{3} \right)}}{7}$$
=
=
/ ___\ / ___\
___ |\/ 7 | ___ |\/ 7 |
2*\/ 7 *atanh|-----| 2*\/ 7 *atanh|-----|
\ 4 / \ 3 /
- -------------------- + --------------------
7 7
$$- \frac{2 \sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7}}{4} \right)}}{7} + \frac{2 \sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7}}{3} \right)}}{7}$$
-2*sqrt(7)*atanh(sqrt(7)/4)/7 + 2*sqrt(7)*atanh(sqrt(7)/3)/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.