Sr Examen
Integral de (4*x+1)/(x^2-9*x+5) dx
Solución
Ha introducido
[src]
oo / | | 4*x + 1 | ------------ dx | 2 | x - 9*x + 5 | / 2
$$\int\limits_{2}^{\infty} \frac{4 x + 1}{\left(x^{2} - 9 x\right) + 5}\, dx$$
Integral((4*x + 1)/(x^2 - 9*x + 5), (x, 2, oo))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 61 *(-9/2 + x)| |
||-\/ 61 *acoth|-------------------| |
/ || \ 61 / 2 |
| ||----------------------------------- for (-9/2 + x) > 61/4|
| 4*x + 1 / 2 \ || 122 |
| ------------ dx = C + 2*log\5 + x - 9*x/ + 76*|< |
| 2 || / ____ \ |
| x - 9*x + 5 || ____ |2*\/ 61 *(-9/2 + x)| |
| ||-\/ 61 *atanh|-------------------| |
/ || \ 61 / 2 |
||----------------------------------- for (-9/2 + x) < 61/4|
\\ 122 /
$$\int \frac{4 x + 1}{\left(x^{2} - 9 x\right) + 5}\, dx = C + 76 \left(\begin{cases} - \frac{\sqrt{61} \operatorname{acoth}{\left(\frac{2 \sqrt{61} \left(x - \frac{9}{2}\right)}{61} \right)}}{122} & \text{for}\: \left(x - \frac{9}{2}\right)^{2} > \frac{61}{4} \\- \frac{\sqrt{61} \operatorname{atanh}{\left(\frac{2 \sqrt{61} \left(x - \frac{9}{2}\right)}{61} \right)}}{122} & \text{for}\: \left(x - \frac{9}{2}\right)^{2} < \frac{61}{4} \end{cases}\right) + 2 \log{\left(x^{2} - 9 x + 5 \right)}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.