Sr Examen
Integral de (1-x)/(4*x^2+4*x-5) dx
Solución
Ha introducido
[src]
1 / | | 1 - x | -------------- dx | 2 | 4*x + 4*x - 5 | / 0
$$\int\limits_{0}^{1} \frac{1 - x}{\left(4 x^{2} + 4 x\right) - 5}\, dx$$
Integral((1 - x)/(4*x^2 + 4*x - 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 6 *(1/2 + x)| |
||-\/ 6 *acoth|---------------| |
|| \ 3 / 2 |
||------------------------------ for (1/2 + x) > 3/2|
|| 6 |
3*|< |
|| / ___ \ |
|| ___ |\/ 6 *(1/2 + x)| |
||-\/ 6 *atanh|---------------| |
/ || \ 3 / 2 |
| / 2\ ||------------------------------ for (1/2 + x) < 3/2|
| 1 - x log\-5 + 4*x + 4*x / \\ 6 /
| -------------- dx = C - -------------------- + ---------------------------------------------------------
| 2 8 4
| 4*x + 4*x - 5
|
/
$$\int \frac{1 - x}{\left(4 x^{2} + 4 x\right) - 5}\, dx = C + \frac{3 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x + \frac{1}{2}\right)}{3} \right)}}{6} & \text{for}\: \left(x + \frac{1}{2}\right)^{2} > \frac{3}{2} \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x + \frac{1}{2}\right)}{3} \right)}}{6} & \text{for}\: \left(x + \frac{1}{2}\right)^{2} < \frac{3}{2} \end{cases}\right)}{4} - \frac{\log{\left(4 x^{2} + 4 x - 5 \right)}}{8}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.