Sr Examen
Integral de 1/(5x^3-4x^2-12x-3) dx
Solución
Ha introducido
[src]
0 / | | 1 | ---------------------- dx | 3 2 | 5*x - 4*x - 12*x - 3 | / 0
$$\int\limits_{0}^{0} \frac{1}{\left(- 12 x + \left(5 x^{3} - 4 x^{2}\right)\right) - 3}\, dx$$
Integral(1/(5*x^3 - 4*x^2 - 12*x - 3), (x, 0, 0))
Respuesta (Indefinida)
[src]
// / _____ \ \
|| _____ |10*\/ 141 *(-9/10 + x)| |
||-\/ 141 *acoth|----------------------| |
|| \ 141 / 2 141|
||--------------------------------------- for (-9/10 + x) > ---|
|| 1410 100|
190*|< |
|| / _____ \ |
|| _____ |10*\/ 141 *(-9/10 + x)| |
||-\/ 141 *atanh|----------------------| |
/ || \ 141 / 2 141|
| / 2\ ||--------------------------------------- for (-9/10 + x) < ---|
| 1 log\-3 - 9*x + 5*x / log(1 + x) \\ 1410 100/
| ---------------------- dx = C - -------------------- + ---------- + ----------------------------------------------------------------------
| 3 2 22 11 11
| 5*x - 4*x - 12*x - 3
|
/
$$\int \frac{1}{\left(- 12 x + \left(5 x^{3} - 4 x^{2}\right)\right) - 3}\, dx = C + \frac{190 \left(\begin{cases} - \frac{\sqrt{141} \operatorname{acoth}{\left(\frac{10 \sqrt{141} \left(x - \frac{9}{10}\right)}{141} \right)}}{1410} & \text{for}\: \left(x - \frac{9}{10}\right)^{2} > \frac{141}{100} \\- \frac{\sqrt{141} \operatorname{atanh}{\left(\frac{10 \sqrt{141} \left(x - \frac{9}{10}\right)}{141} \right)}}{1410} & \text{for}\: \left(x - \frac{9}{10}\right)^{2} < \frac{141}{100} \end{cases}\right)}{11} + \frac{\log{\left(x + 1 \right)}}{11} - \frac{\log{\left(5 x^{2} - 9 x - 3 \right)}}{22}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.