Sr Examen
Integral de (5x-1)/(2x^2-x-7) dx
Solución
Ha introducido
[src]
1 / | | 5*x - 1 | ------------ dx | 2 | 2*x - x - 7 | / 0
$$\int\limits_{0}^{1} \frac{5 x - 1}{\left(2 x^{2} - x\right) - 7}\, dx$$
Integral((5*x - 1)/(2*x^2 - x - 7), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |4*\/ 57 *(-1/4 + x)| |
||-\/ 57 *acoth|-------------------| |
/ || \ 57 / 2 57|
| ||----------------------------------- for (-1/4 + x) > --| / 2\
| 5*x - 1 || 228 16| 5*log\-7 - x + 2*x /
| ------------ dx = C + 2*|< | + --------------------
| 2 || / ____ \ | 4
| 2*x - x - 7 || ____ |4*\/ 57 *(-1/4 + x)| |
| ||-\/ 57 *atanh|-------------------| |
/ || \ 57 / 2 57|
||----------------------------------- for (-1/4 + x) < --|
\\ 228 16/
$$\int \frac{5 x - 1}{\left(2 x^{2} - x\right) - 7}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{57} \operatorname{acoth}{\left(\frac{4 \sqrt{57} \left(x - \frac{1}{4}\right)}{57} \right)}}{228} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} > \frac{57}{16} \\- \frac{\sqrt{57} \operatorname{atanh}{\left(\frac{4 \sqrt{57} \left(x - \frac{1}{4}\right)}{57} \right)}}{228} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} < \frac{57}{16} \end{cases}\right) + \frac{5 \log{\left(2 x^{2} - x - 7 \right)}}{4}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ |5 \/ 57 | |3 \/ 57 | |5 \/ 57 | | | 3 \/ 57 || |5 \/ 57 | | 1 \/ 57 | |5 \/ 57 | | |1 \/ 57 || |- - ------|*log|- + ------| + |- + ------|*|pi*I + log|- - + ------|| - |- - ------|*log|- - + ------| - |- + ------|*|pi*I + log|- + ------|| \4 228 / \4 4 / \4 228 / \ \ 4 4 // \4 228 / \ 4 4 / \4 228 / \ \4 4 //
$$- \left(\frac{5}{4} - \frac{\sqrt{57}}{228}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{57}}{4} \right)} + \left(\frac{5}{4} - \frac{\sqrt{57}}{228}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{57}}{4} \right)} - \left(\frac{\sqrt{57}}{228} + \frac{5}{4}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{57}}{4} \right)} + i \pi\right) + \left(\frac{\sqrt{57}}{228} + \frac{5}{4}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{57}}{4} \right)} + i \pi\right)$$
=
=
/ ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ |5 \/ 57 | |3 \/ 57 | |5 \/ 57 | | | 3 \/ 57 || |5 \/ 57 | | 1 \/ 57 | |5 \/ 57 | | |1 \/ 57 || |- - ------|*log|- + ------| + |- + ------|*|pi*I + log|- - + ------|| - |- - ------|*log|- - + ------| - |- + ------|*|pi*I + log|- + ------|| \4 228 / \4 4 / \4 228 / \ \ 4 4 // \4 228 / \ 4 4 / \4 228 / \ \4 4 //
$$- \left(\frac{5}{4} - \frac{\sqrt{57}}{228}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{57}}{4} \right)} + \left(\frac{5}{4} - \frac{\sqrt{57}}{228}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{57}}{4} \right)} - \left(\frac{\sqrt{57}}{228} + \frac{5}{4}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{57}}{4} \right)} + i \pi\right) + \left(\frac{\sqrt{57}}{228} + \frac{5}{4}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{57}}{4} \right)} + i \pi\right)$$
(5/4 - sqrt(57)/228)*log(3/4 + sqrt(57)/4) + (5/4 + sqrt(57)/228)*(pi*i + log(-3/4 + sqrt(57)/4)) - (5/4 - sqrt(57)/228)*log(-1/4 + sqrt(57)/4) - (5/4 + sqrt(57)/228)*(pi*i + log(1/4 + sqrt(57)/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.