Sr Examen
Integral de 1/(x^2+9x+13) dx
Solución
Ha introducido
[src]
-1 / | | 1 | ------------- dx | 2 | x + 9*x + 13 | / -oo
$$\int\limits_{-\infty}^{-1} \frac{1}{\left(x^{2} + 9 x\right) + 13}\, dx$$
Integral(1/(x^2 + 9*x + 13), (x, -oo, -1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 29 *(9/2 + x)| |
||-\/ 29 *acoth|------------------| |
/ || \ 29 / 2 |
| ||---------------------------------- for (9/2 + x) > 29/4|
| 1 || 58 |
| ------------- dx = C + 4*|< |
| 2 || / ____ \ |
| x + 9*x + 13 || ____ |2*\/ 29 *(9/2 + x)| |
| ||-\/ 29 *atanh|------------------| |
/ || \ 29 / 2 |
||---------------------------------- for (9/2 + x) < 29/4|
\\ 58 /
$$\int \frac{1}{\left(x^{2} + 9 x\right) + 13}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{29} \operatorname{acoth}{\left(\frac{2 \sqrt{29} \left(x + \frac{9}{2}\right)}{29} \right)}}{58} & \text{for}\: \left(x + \frac{9}{2}\right)^{2} > \frac{29}{4} \\- \frac{\sqrt{29} \operatorname{atanh}{\left(\frac{2 \sqrt{29} \left(x + \frac{9}{2}\right)}{29} \right)}}{58} & \text{for}\: \left(x + \frac{9}{2}\right)^{2} < \frac{29}{4} \end{cases}\right)$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.