Sr Examen
Integral de dx/(x^2-16*x-16) dx
Solución
Ha introducido
[src]
16 / | | 1 | -------------- dx | 2 | x - 16*x - 16 | / 3
$$\int\limits_{3}^{16} \frac{1}{\left(x^{2} - 16 x\right) - 16}\, dx$$
Integral(1/(x^2 - 16*x - 16), (x, 3, 16))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 5 *(-8 + x)| |
||-\/ 5 *acoth|--------------| |
/ || \ 20 / 2 |
| ||----------------------------- for (-8 + x) > 80|
| 1 || 20 |
| -------------- dx = C + |< |
| 2 || / ___ \ |
| x - 16*x - 16 || ___ |\/ 5 *(-8 + x)| |
| ||-\/ 5 *atanh|--------------| |
/ || \ 20 / 2 |
||----------------------------- for (-8 + x) < 80|
\\ 20 /
$$\int \frac{1}{\left(x^{2} - 16 x\right) - 16}\, dx = C + \begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \left(x - 8\right)}{20} \right)}}{20} & \text{for}\: \left(x - 8\right)^{2} > 80 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \left(x - 8\right)}{20} \right)}}{20} & \text{for}\: \left(x - 8\right)^{2} < 80 \end{cases}$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 5 *\pi*I + log\5 + 4*\/ 5 // \/ 5 *log\8 + 4*\/ 5 / \/ 5 *\pi*I + log\-8 + 4*\/ 5 // \/ 5 *log\-5 + 4*\/ 5 /
- ------------------------------- - ---------------------- + -------------------------------- + -----------------------
40 40 40 40
$$- \frac{\sqrt{5} \log{\left(8 + 4 \sqrt{5} \right)}}{40} + \frac{\sqrt{5} \log{\left(-5 + 4 \sqrt{5} \right)}}{40} - \frac{\sqrt{5} \left(\log{\left(5 + 4 \sqrt{5} \right)} + i \pi\right)}{40} + \frac{\sqrt{5} \left(\log{\left(-8 + 4 \sqrt{5} \right)} + i \pi\right)}{40}$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 5 *\pi*I + log\5 + 4*\/ 5 // \/ 5 *log\8 + 4*\/ 5 / \/ 5 *\pi*I + log\-8 + 4*\/ 5 // \/ 5 *log\-5 + 4*\/ 5 /
- ------------------------------- - ---------------------- + -------------------------------- + -----------------------
40 40 40 40
$$- \frac{\sqrt{5} \log{\left(8 + 4 \sqrt{5} \right)}}{40} + \frac{\sqrt{5} \log{\left(-5 + 4 \sqrt{5} \right)}}{40} - \frac{\sqrt{5} \left(\log{\left(5 + 4 \sqrt{5} \right)} + i \pi\right)}{40} + \frac{\sqrt{5} \left(\log{\left(-8 + 4 \sqrt{5} \right)} + i \pi\right)}{40}$$
-sqrt(5)*(pi*i + log(5 + 4*sqrt(5)))/40 - sqrt(5)*log(8 + 4*sqrt(5))/40 + sqrt(5)*(pi*i + log(-8 + 4*sqrt(5)))/40 + sqrt(5)*log(-5 + 4*sqrt(5))/40
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.