Sr Examen
Integral de (3x+1)/(3x^2-2x-3) dx
Solución
Ha introducido
[src]
oo / | | 3*x + 1 | -------------- dx | 2 | 3*x - 2*x - 3 | / 0
$$\int\limits_{0}^{\infty} \frac{3 x + 1}{\left(3 x^{2} - 2 x\right) - 3}\, dx$$
Integral((3*x + 1)/(3*x^2 - 2*x - 3), (x, 0, oo))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |3*\/ 10 *(-1/3 + x)| |
||-\/ 10 *acoth|-------------------| |
/ || \ 10 / 2 |
| / 2\ ||----------------------------------- for (-1/3 + x) > 10/9|
| 3*x + 1 log\-3 - 2*x + 3*x / || 30 |
| -------------- dx = C + -------------------- + 6*|< |
| 2 2 || / ____ \ |
| 3*x - 2*x - 3 || ____ |3*\/ 10 *(-1/3 + x)| |
| ||-\/ 10 *atanh|-------------------| |
/ || \ 10 / 2 |
||----------------------------------- for (-1/3 + x) < 10/9|
\\ 30 /
$$\int \frac{3 x + 1}{\left(3 x^{2} - 2 x\right) - 3}\, dx = C + 6 \left(\begin{cases} - \frac{\sqrt{10} \operatorname{acoth}{\left(\frac{3 \sqrt{10} \left(x - \frac{1}{3}\right)}{10} \right)}}{30} & \text{for}\: \left(x - \frac{1}{3}\right)^{2} > \frac{10}{9} \\- \frac{\sqrt{10} \operatorname{atanh}{\left(\frac{3 \sqrt{10} \left(x - \frac{1}{3}\right)}{10} \right)}}{30} & \text{for}\: \left(x - \frac{1}{3}\right)^{2} < \frac{10}{9} \end{cases}\right) + \frac{\log{\left(3 x^{2} - 2 x - 3 \right)}}{2}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.