Sr Examen
Integral de (2+x)/(-x^2-5x-1) dx
Solución
Ha introducido
[src]
1 / | | 2 + x | -------------- dx | 2 | - x - 5*x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x + 2}{\left(- x^{2} - 5 x\right) - 1}\, dx$$
Integral((2 + x)/(-x^2 - 5*x - 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 21 *(5/2 + x)| |
||-\/ 21 *acoth|------------------| |
/ || \ 21 / 2 |
| ||---------------------------------- for (5/2 + x) > 21/4| / 2 \
| 2 + x || 42 | log\-1 - x - 5*x/
| -------------- dx = C + 2*|< | - ------------------
| 2 || / ____ \ | 2
| - x - 5*x - 1 || ____ |2*\/ 21 *(5/2 + x)| |
| ||-\/ 21 *atanh|------------------| |
/ || \ 21 / 2 |
||---------------------------------- for (5/2 + x) < 21/4|
\\ 42 /
$$\int \frac{x + 2}{\left(- x^{2} - 5 x\right) - 1}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{21} \operatorname{acoth}{\left(\frac{2 \sqrt{21} \left(x + \frac{5}{2}\right)}{21} \right)}}{42} & \text{for}\: \left(x + \frac{5}{2}\right)^{2} > \frac{21}{4} \\- \frac{\sqrt{21} \operatorname{atanh}{\left(\frac{2 \sqrt{21} \left(x + \frac{5}{2}\right)}{21} \right)}}{42} & \text{for}\: \left(x + \frac{5}{2}\right)^{2} < \frac{21}{4} \end{cases}\right) - \frac{\log{\left(- x^{2} - 5 x - 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ |1 \/ 21 | |5 \/ 21 | |1 \/ 21 | |5 \/ 21 | |1 \/ 21 | |7 \/ 21 | |1 \/ 21 | |7 \/ 21 | |- - ------|*log|- - ------| + |- + ------|*log|- + ------| - |- - ------|*log|- - ------| - |- + ------|*log|- + ------| \2 42 / \2 2 / \2 42 / \2 2 / \2 42 / \2 2 / \2 42 / \2 2 /
$$- \left(\frac{\sqrt{21}}{42} + \frac{1}{2}\right) \log{\left(\frac{\sqrt{21}}{2} + \frac{7}{2} \right)} + \left(\frac{1}{2} - \frac{\sqrt{21}}{42}\right) \log{\left(\frac{5}{2} - \frac{\sqrt{21}}{2} \right)} - \left(\frac{1}{2} - \frac{\sqrt{21}}{42}\right) \log{\left(\frac{7}{2} - \frac{\sqrt{21}}{2} \right)} + \left(\frac{\sqrt{21}}{42} + \frac{1}{2}\right) \log{\left(\frac{\sqrt{21}}{2} + \frac{5}{2} \right)}$$
=
=
/ ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ |1 \/ 21 | |5 \/ 21 | |1 \/ 21 | |5 \/ 21 | |1 \/ 21 | |7 \/ 21 | |1 \/ 21 | |7 \/ 21 | |- - ------|*log|- - ------| + |- + ------|*log|- + ------| - |- - ------|*log|- - ------| - |- + ------|*log|- + ------| \2 42 / \2 2 / \2 42 / \2 2 / \2 42 / \2 2 / \2 42 / \2 2 /
$$- \left(\frac{\sqrt{21}}{42} + \frac{1}{2}\right) \log{\left(\frac{\sqrt{21}}{2} + \frac{7}{2} \right)} + \left(\frac{1}{2} - \frac{\sqrt{21}}{42}\right) \log{\left(\frac{5}{2} - \frac{\sqrt{21}}{2} \right)} - \left(\frac{1}{2} - \frac{\sqrt{21}}{42}\right) \log{\left(\frac{7}{2} - \frac{\sqrt{21}}{2} \right)} + \left(\frac{\sqrt{21}}{42} + \frac{1}{2}\right) \log{\left(\frac{\sqrt{21}}{2} + \frac{5}{2} \right)}$$
(1/2 - sqrt(21)/42)*log(5/2 - sqrt(21)/2) + (1/2 + sqrt(21)/42)*log(5/2 + sqrt(21)/2) - (1/2 - sqrt(21)/42)*log(7/2 - sqrt(21)/2) - (1/2 + sqrt(21)/42)*log(7/2 + sqrt(21)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.