Sr Examen
Integral de dx/(x^2+x-13) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | 2 | x + x - 13 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + x\right) - 13}\, dx$$
Integral(1/(x^2 + x - 13), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 53 *(1/2 + x)| |
||-\/ 53 *acoth|------------------| |
/ || \ 53 / 2 |
| ||---------------------------------- for (1/2 + x) > 53/4|
| 1 || 106 |
| ----------- dx = C + 4*|< |
| 2 || / ____ \ |
| x + x - 13 || ____ |2*\/ 53 *(1/2 + x)| |
| ||-\/ 53 *atanh|------------------| |
/ || \ 53 / 2 |
||---------------------------------- for (1/2 + x) < 53/4|
\\ 106 /
$$\int \frac{1}{\left(x^{2} + x\right) - 13}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{53} \operatorname{acoth}{\left(\frac{2 \sqrt{53} \left(x + \frac{1}{2}\right)}{53} \right)}}{106} & \text{for}\: \left(x + \frac{1}{2}\right)^{2} > \frac{53}{4} \\- \frac{\sqrt{53} \operatorname{atanh}{\left(\frac{2 \sqrt{53} \left(x + \frac{1}{2}\right)}{53} \right)}}{106} & \text{for}\: \left(x + \frac{1}{2}\right)^{2} < \frac{53}{4} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | 1 \/ 53 || ____ |3 \/ 53 | ____ | | 3 \/ 53 || ____ |1 \/ 53 |
\/ 53 *|pi*I + log|- - + ------|| \/ 53 *log|- + ------| \/ 53 *|pi*I + log|- - + ------|| \/ 53 *log|- + ------|
\ \ 2 2 // \2 2 / \ \ 2 2 // \2 2 /
- --------------------------------- - ---------------------- + --------------------------------- + ----------------------
53 53 53 53
$$- \frac{\sqrt{53} \log{\left(\frac{3}{2} + \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{1}{2} + \frac{\sqrt{53}}{2} \right)}}{53} - \frac{\sqrt{53} \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{53}}{2} \right)} + i \pi\right)}{53} + \frac{\sqrt{53} \left(\log{\left(- \frac{3}{2} + \frac{\sqrt{53}}{2} \right)} + i \pi\right)}{53}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | 1 \/ 53 || ____ |3 \/ 53 | ____ | | 3 \/ 53 || ____ |1 \/ 53 |
\/ 53 *|pi*I + log|- - + ------|| \/ 53 *log|- + ------| \/ 53 *|pi*I + log|- - + ------|| \/ 53 *log|- + ------|
\ \ 2 2 // \2 2 / \ \ 2 2 // \2 2 /
- --------------------------------- - ---------------------- + --------------------------------- + ----------------------
53 53 53 53
$$- \frac{\sqrt{53} \log{\left(\frac{3}{2} + \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{1}{2} + \frac{\sqrt{53}}{2} \right)}}{53} - \frac{\sqrt{53} \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{53}}{2} \right)} + i \pi\right)}{53} + \frac{\sqrt{53} \left(\log{\left(- \frac{3}{2} + \frac{\sqrt{53}}{2} \right)} + i \pi\right)}{53}$$
-sqrt(53)*(pi*i + log(-1/2 + sqrt(53)/2))/53 - sqrt(53)*log(3/2 + sqrt(53)/2)/53 + sqrt(53)*(pi*i + log(-3/2 + sqrt(53)/2))/53 + sqrt(53)*log(1/2 + sqrt(53)/2)/53
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.