Sr Examen
Integral de dx/(x^2-2*x-4) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 2 | x - 2*x - 4 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 2 x\right) - 4}\, dx$$
Integral(1/(x^2 - 2*x - 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 5 *(-1 + x)| |
||-\/ 5 *acoth|--------------| |
/ || \ 5 / 2 |
| ||----------------------------- for (-1 + x) > 5|
| 1 || 5 |
| ------------ dx = C + |< |
| 2 || / ___ \ |
| x - 2*x - 4 || ___ |\/ 5 *(-1 + x)| |
| ||-\/ 5 *atanh|--------------| |
/ || \ 5 / 2 |
||----------------------------- for (-1 + x) < 5|
\\ 5 /
$$\int \frac{1}{\left(x^{2} - 2 x\right) - 4}\, dx = C + \begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \left(x - 1\right)}{5} \right)}}{5} & \text{for}\: \left(x - 1\right)^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \left(x - 1\right)}{5} \right)}}{5} & \text{for}\: \left(x - 1\right)^{2} < 5 \end{cases}$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 5 *\pi*I + log\1 + \/ 5 // \/ 5 *log\\/ 5 / \/ 5 *\pi*I + log\\/ 5 // \/ 5 *log\-1 + \/ 5 /
- ----------------------------- - ---------------- + ------------------------- + ---------------------
10 10 10 10
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(-1 + \sqrt{5} \right)}}{10} - \frac{\sqrt{5} \left(\log{\left(1 + \sqrt{5} \right)} + i \pi\right)}{10} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{10}$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 5 *\pi*I + log\1 + \/ 5 // \/ 5 *log\\/ 5 / \/ 5 *\pi*I + log\\/ 5 // \/ 5 *log\-1 + \/ 5 /
- ----------------------------- - ---------------- + ------------------------- + ---------------------
10 10 10 10
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(-1 + \sqrt{5} \right)}}{10} - \frac{\sqrt{5} \left(\log{\left(1 + \sqrt{5} \right)} + i \pi\right)}{10} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{10}$$
-sqrt(5)*(pi*i + log(1 + sqrt(5)))/10 - sqrt(5)*log(sqrt(5))/10 + sqrt(5)*(pi*i + log(sqrt(5)))/10 + sqrt(5)*log(-1 + sqrt(5))/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.