Sr Examen
Integral de (2*x-1)/(3*x^2-2*x-6) dx
Solución
Ha introducido
[src]
1 / | | 2*x - 1 | -------------- dx | 2 | 3*x - 2*x - 6 | / 0
$$\int\limits_{0}^{1} \frac{2 x - 1}{\left(3 x^{2} - 2 x\right) - 6}\, dx$$
Integral((2*x - 1)/(3*x^2 - 2*x - 6), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |3*\/ 19 *(-1/3 + x)| |
||-\/ 19 *acoth|-------------------| |
/ || \ 19 / 2 |
| ||----------------------------------- for (-1/3 + x) > 19/9| / 2\
| 2*x - 1 || 57 | log\-6 - 2*x + 3*x /
| -------------- dx = C - |< | + --------------------
| 2 || / ____ \ | 3
| 3*x - 2*x - 6 || ____ |3*\/ 19 *(-1/3 + x)| |
| ||-\/ 19 *atanh|-------------------| |
/ || \ 19 / 2 |
||----------------------------------- for (-1/3 + x) < 19/9|
\\ 57 /
$$\int \frac{2 x - 1}{\left(3 x^{2} - 2 x\right) - 6}\, dx = C - \begin{cases} - \frac{\sqrt{19} \operatorname{acoth}{\left(\frac{3 \sqrt{19} \left(x - \frac{1}{3}\right)}{19} \right)}}{57} & \text{for}\: \left(x - \frac{1}{3}\right)^{2} > \frac{19}{9} \\- \frac{\sqrt{19} \operatorname{atanh}{\left(\frac{3 \sqrt{19} \left(x - \frac{1}{3}\right)}{19} \right)}}{57} & \text{for}\: \left(x - \frac{1}{3}\right)^{2} < \frac{19}{9} \end{cases} + \frac{\log{\left(3 x^{2} - 2 x - 6 \right)}}{3}$$
Gráfica
Respuesta
[src]
/ ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ |1 \/ 19 | | | 2 \/ 19 || |1 \/ 19 | |2 \/ 19 | |1 \/ 19 | | |1 \/ 19 || |1 \/ 19 | | 1 \/ 19 | |- - ------|*|pi*I + log|- - + ------|| + |- + ------|*log|- + ------| - |- - ------|*|pi*I + log|- + ------|| - |- + ------|*log|- - + ------| \3 114 / \ \ 3 3 // \3 114 / \3 3 / \3 114 / \ \3 3 // \3 114 / \ 3 3 /
$$- \left(\frac{\sqrt{19}}{114} + \frac{1}{3}\right) \log{\left(- \frac{1}{3} + \frac{\sqrt{19}}{3} \right)} + \left(\frac{\sqrt{19}}{114} + \frac{1}{3}\right) \log{\left(\frac{2}{3} + \frac{\sqrt{19}}{3} \right)} - \left(\frac{1}{3} - \frac{\sqrt{19}}{114}\right) \left(\log{\left(\frac{1}{3} + \frac{\sqrt{19}}{3} \right)} + i \pi\right) + \left(\frac{1}{3} - \frac{\sqrt{19}}{114}\right) \left(\log{\left(- \frac{2}{3} + \frac{\sqrt{19}}{3} \right)} + i \pi\right)$$
=
=
/ ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ |1 \/ 19 | | | 2 \/ 19 || |1 \/ 19 | |2 \/ 19 | |1 \/ 19 | | |1 \/ 19 || |1 \/ 19 | | 1 \/ 19 | |- - ------|*|pi*I + log|- - + ------|| + |- + ------|*log|- + ------| - |- - ------|*|pi*I + log|- + ------|| - |- + ------|*log|- - + ------| \3 114 / \ \ 3 3 // \3 114 / \3 3 / \3 114 / \ \3 3 // \3 114 / \ 3 3 /
$$- \left(\frac{\sqrt{19}}{114} + \frac{1}{3}\right) \log{\left(- \frac{1}{3} + \frac{\sqrt{19}}{3} \right)} + \left(\frac{\sqrt{19}}{114} + \frac{1}{3}\right) \log{\left(\frac{2}{3} + \frac{\sqrt{19}}{3} \right)} - \left(\frac{1}{3} - \frac{\sqrt{19}}{114}\right) \left(\log{\left(\frac{1}{3} + \frac{\sqrt{19}}{3} \right)} + i \pi\right) + \left(\frac{1}{3} - \frac{\sqrt{19}}{114}\right) \left(\log{\left(- \frac{2}{3} + \frac{\sqrt{19}}{3} \right)} + i \pi\right)$$
(1/3 - sqrt(19)/114)*(pi*i + log(-2/3 + sqrt(19)/3)) + (1/3 + sqrt(19)/114)*log(2/3 + sqrt(19)/3) - (1/3 - sqrt(19)/114)*(pi*i + log(1/3 + sqrt(19)/3)) - (1/3 + sqrt(19)/114)*log(-1/3 + sqrt(19)/3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.