Sr Examen
Integral de 1/((x-1)*(x^2-6x-8)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ---------------------- dx | / 2 \ | (x - 1)*\x - 6*x - 8/ | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x - 1\right) \left(\left(x^{2} - 6 x\right) - 8\right)}\, dx$$
Integral(1/((x - 1)*(x^2 - 6*x - 8)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |\/ 17 *(-3 + x)| |
||-\/ 17 *acoth|---------------| |
|| \ 17 / 2 |
||------------------------------- for (-3 + x) > 17|
|| 17 |
2*|< |
|| / ____ \ |
|| ____ |\/ 17 *(-3 + x)| |
||-\/ 17 *atanh|---------------| |
/ || \ 17 / 2 |
| ||------------------------------- for (-3 + x) < 17| / 2 \
| 1 \\ 17 / log(-1 + x) log\-8 + x - 6*x/
| ---------------------- dx = C - -------------------------------------------------------- - ----------- + ------------------
| / 2 \ 13 13 26
| (x - 1)*\x - 6*x - 8/
|
/
$$\int \frac{1}{\left(x - 1\right) \left(\left(x^{2} - 6 x\right) - 8\right)}\, dx = C - \frac{2 \left(\begin{cases} - \frac{\sqrt{17} \operatorname{acoth}{\left(\frac{\sqrt{17} \left(x - 3\right)}{17} \right)}}{17} & \text{for}\: \left(x - 3\right)^{2} > 17 \\- \frac{\sqrt{17} \operatorname{atanh}{\left(\frac{\sqrt{17} \left(x - 3\right)}{17} \right)}}{17} & \text{for}\: \left(x - 3\right)^{2} < 17 \end{cases}\right)}{13} - \frac{\log{\left(x - 1 \right)}}{13} + \frac{\log{\left(x^{2} - 6 x - 8 \right)}}{26}$$
Gráfica
Respuesta
[src]
/ / 2 \\
| | / ____\ ||
| | |1 \/ 17 | ||
/ ____\ | | 316030*|-- - ------| ____||
|1 \/ 17 | | |2049 \26 221 / 39*\/ 17 || pi*I
oo - |-- - ------|*|pi*I + log|---- - --------------------- + ---------|| + ----
\26 221 / \ \298 149 149 // 13
$$\infty - \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right) \left(\log{\left(- \frac{316030 \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right)^{2}}{149} + \frac{39 \sqrt{17}}{149} + \frac{2049}{298} \right)} + i \pi\right) + \frac{i \pi}{13}$$
=
=
/ / 2 \\
| | / ____\ ||
| | |1 \/ 17 | ||
/ ____\ | | 316030*|-- - ------| ____||
|1 \/ 17 | | |2049 \26 221 / 39*\/ 17 || pi*I
oo - |-- - ------|*|pi*I + log|---- - --------------------- + ---------|| + ----
\26 221 / \ \298 149 149 // 13
$$\infty - \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right) \left(\log{\left(- \frac{316030 \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right)^{2}}{149} + \frac{39 \sqrt{17}}{149} + \frac{2049}{298} \right)} + i \pi\right) + \frac{i \pi}{13}$$
oo - (1/26 - sqrt(17)/221)*(pi*i + log(2049/298 - 316030*(1/26 - sqrt(17)/221)^2/149 + 39*sqrt(17)/149)) + pi*i/13
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.