Sr Examen
Integral de (2*x^3-3*x+2)/(x^2+6*x-4) dx
Solución
Ha introducido
[src]
1 / | | 3 | 2*x - 3*x + 2 | -------------- dx | 2 | x + 6*x - 4 | / 0
$$\int\limits_{0}^{1} \frac{\left(2 x^{3} - 3 x\right) + 2}{\left(x^{2} + 6 x\right) - 4}\, dx$$
Integral((2*x^3 - 3*x + 2)/(x^2 + 6*x - 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |\/ 13 *(3 + x)| |
/ ||-\/ 13 *acoth|--------------| |
| || \ 13 / 2 |
| 3 ||------------------------------ for (3 + x) > 13| / 2 \
| 2*x - 3*x + 2 2 || 13 | 77*log\-4 + x + 6*x/
| -------------- dx = C + x - 277*|< | - 12*x + ---------------------
| 2 || / ____ \ | 2
| x + 6*x - 4 || ____ |\/ 13 *(3 + x)| |
| ||-\/ 13 *atanh|--------------| |
/ || \ 13 / 2 |
||------------------------------ for (3 + x) < 13|
\\ 13 /
$$\int \frac{\left(2 x^{3} - 3 x\right) + 2}{\left(x^{2} + 6 x\right) - 4}\, dx = C + x^{2} - 12 x - 277 \left(\begin{cases} - \frac{\sqrt{13} \operatorname{acoth}{\left(\frac{\sqrt{13} \left(x + 3\right)}{13} \right)}}{13} & \text{for}\: \left(x + 3\right)^{2} > 13 \\- \frac{\sqrt{13} \operatorname{atanh}{\left(\frac{\sqrt{13} \left(x + 3\right)}{13} \right)}}{13} & \text{for}\: \left(x + 3\right)^{2} < 13 \end{cases}\right) + \frac{77 \log{\left(x^{2} + 6 x - 4 \right)}}{2}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.