Sr Examen
Integral de (2x-5)/(2x^2-x-4) dx
Solución
Ha introducido
[src]
1 / | | 2*x - 5 | ------------ dx | 2 | 2*x - x - 4 | / 0
$$\int\limits_{0}^{1} \frac{2 x - 5}{\left(2 x^{2} - x\right) - 4}\, dx$$
Integral((2*x - 5)/(2*x^2 - x - 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |4*\/ 33 *(-1/4 + x)| |
||-\/ 33 *acoth|-------------------| |
/ || \ 33 / 2 33|
| / 2\ ||----------------------------------- for (-1/4 + x) > --|
| 2*x - 5 log\-4 - x + 2*x / || 132 16|
| ------------ dx = C + ------------------ - 36*|< |
| 2 2 || / ____ \ |
| 2*x - x - 4 || ____ |4*\/ 33 *(-1/4 + x)| |
| ||-\/ 33 *atanh|-------------------| |
/ || \ 33 / 2 33|
||----------------------------------- for (-1/4 + x) < --|
\\ 132 16/
$$\int \frac{2 x - 5}{\left(2 x^{2} - x\right) - 4}\, dx = C - 36 \left(\begin{cases} - \frac{\sqrt{33} \operatorname{acoth}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} > \frac{33}{16} \\- \frac{\sqrt{33} \operatorname{atanh}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} < \frac{33}{16} \end{cases}\right) + \frac{\log{\left(2 x^{2} - x - 4 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ |1 3*\/ 33 | | | 3 \/ 33 || |1 3*\/ 33 | |3 \/ 33 | |1 3*\/ 33 | | |1 \/ 33 || |1 3*\/ 33 | | 1 \/ 33 | |- - --------|*|pi*I + log|- - + ------|| + |- + --------|*log|- + ------| - |- - --------|*|pi*I + log|- + ------|| - |- + --------|*log|- - + ------| \2 22 / \ \ 4 4 // \2 22 / \4 4 / \2 22 / \ \4 4 // \2 22 / \ 4 4 /
$$- \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) - \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)$$
=
=
/ ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ |1 3*\/ 33 | | | 3 \/ 33 || |1 3*\/ 33 | |3 \/ 33 | |1 3*\/ 33 | | |1 \/ 33 || |1 3*\/ 33 | | 1 \/ 33 | |- - --------|*|pi*I + log|- - + ------|| + |- + --------|*log|- + ------| - |- - --------|*|pi*I + log|- + ------|| - |- + --------|*log|- - + ------| \2 22 / \ \ 4 4 // \2 22 / \4 4 / \2 22 / \ \4 4 // \2 22 / \ 4 4 /
$$- \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) - \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)$$
(1/2 - 3*sqrt(33)/22)*(pi*i + log(-3/4 + sqrt(33)/4)) + (1/2 + 3*sqrt(33)/22)*log(3/4 + sqrt(33)/4) - (1/2 - 3*sqrt(33)/22)*(pi*i + log(1/4 + sqrt(33)/4)) - (1/2 + 3*sqrt(33)/22)*log(-1/4 + sqrt(33)/4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.