Sr Examen
Integral de dx/(x^2+9*x+7) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 2 | x + 9*x + 7 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 9 x\right) + 7}\, dx$$
Integral(1/(x^2 + 9*x + 7), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 53 *(9/2 + x)| |
||-\/ 53 *acoth|------------------| |
/ || \ 53 / 2 |
| ||---------------------------------- for (9/2 + x) > 53/4|
| 1 || 106 |
| ------------ dx = C + 4*|< |
| 2 || / ____ \ |
| x + 9*x + 7 || ____ |2*\/ 53 *(9/2 + x)| |
| ||-\/ 53 *atanh|------------------| |
/ || \ 53 / 2 |
||---------------------------------- for (9/2 + x) < 53/4|
\\ 106 /
$$\int \frac{1}{\left(x^{2} + 9 x\right) + 7}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{53} \operatorname{acoth}{\left(\frac{2 \sqrt{53} \left(x + \frac{9}{2}\right)}{53} \right)}}{106} & \text{for}\: \left(x + \frac{9}{2}\right)^{2} > \frac{53}{4} \\- \frac{\sqrt{53} \operatorname{atanh}{\left(\frac{2 \sqrt{53} \left(x + \frac{9}{2}\right)}{53} \right)}}{106} & \text{for}\: \left(x + \frac{9}{2}\right)^{2} < \frac{53}{4} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ____\ / ____\ / ____\ / ____\
____ |9 \/ 53 | ____ |11 \/ 53 | ____ |9 \/ 53 | ____ |11 \/ 53 |
\/ 53 *log|- - ------| \/ 53 *log|-- + ------| \/ 53 *log|- + ------| \/ 53 *log|-- - ------|
\2 2 / \2 2 / \2 2 / \2 2 /
- ---------------------- - ----------------------- + ---------------------- + -----------------------
53 53 53 53
$$- \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{11}{2} \right)}}{53} - \frac{\sqrt{53} \log{\left(\frac{9}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{11}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{9}{2} \right)}}{53}$$
=
=
/ ____\ / ____\ / ____\ / ____\
____ |9 \/ 53 | ____ |11 \/ 53 | ____ |9 \/ 53 | ____ |11 \/ 53 |
\/ 53 *log|- - ------| \/ 53 *log|-- + ------| \/ 53 *log|- + ------| \/ 53 *log|-- - ------|
\2 2 / \2 2 / \2 2 / \2 2 /
- ---------------------- - ----------------------- + ---------------------- + -----------------------
53 53 53 53
$$- \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{11}{2} \right)}}{53} - \frac{\sqrt{53} \log{\left(\frac{9}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{11}{2} - \frac{\sqrt{53}}{2} \right)}}{53} + \frac{\sqrt{53} \log{\left(\frac{\sqrt{53}}{2} + \frac{9}{2} \right)}}{53}$$
-sqrt(53)*log(9/2 - sqrt(53)/2)/53 - sqrt(53)*log(11/2 + sqrt(53)/2)/53 + sqrt(53)*log(9/2 + sqrt(53)/2)/53 + sqrt(53)*log(11/2 - sqrt(53)/2)/53
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.