Sr Examen
Integral de 1/(x^2+6*x-2) dx
Solución
Ha introducido
[src]
2 / | | 1 | ------------ dx | 2 | x + 6*x - 2 | / 1
$$\int\limits_{1}^{2} \frac{1}{\left(x^{2} + 6 x\right) - 2}\, dx$$
Integral(1/(x^2 + 6*x - 2), (x, 1, 2))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |\/ 11 *(3 + x)| |
||-\/ 11 *acoth|--------------| |
/ || \ 11 / 2 |
| ||------------------------------ for (3 + x) > 11|
| 1 || 11 |
| ------------ dx = C + |< |
| 2 || / ____ \ |
| x + 6*x - 2 || ____ |\/ 11 *(3 + x)| |
| ||-\/ 11 *atanh|--------------| |
/ || \ 11 / 2 |
||------------------------------ for (3 + x) < 11|
\\ 11 /
$$\int \frac{1}{\left(x^{2} + 6 x\right) - 2}\, dx = C + \begin{cases} - \frac{\sqrt{11} \operatorname{acoth}{\left(\frac{\sqrt{11} \left(x + 3\right)}{11} \right)}}{11} & \text{for}\: \left(x + 3\right)^{2} > 11 \\- \frac{\sqrt{11} \operatorname{atanh}{\left(\frac{\sqrt{11} \left(x + 3\right)}{11} \right)}}{11} & \text{for}\: \left(x + 3\right)^{2} < 11 \end{cases}$$
Gráfica
Respuesta
[src]
____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\
\/ 11 *log\4 - \/ 11 / \/ 11 *log\5 + \/ 11 / \/ 11 *log\4 + \/ 11 / \/ 11 *log\5 - \/ 11 /
- ---------------------- - ---------------------- + ---------------------- + ----------------------
22 22 22 22
$$- \frac{\sqrt{11} \log{\left(\sqrt{11} + 5 \right)}}{22} - \frac{\sqrt{11} \log{\left(4 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(5 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(\sqrt{11} + 4 \right)}}{22}$$
=
=
____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\
\/ 11 *log\4 - \/ 11 / \/ 11 *log\5 + \/ 11 / \/ 11 *log\4 + \/ 11 / \/ 11 *log\5 - \/ 11 /
- ---------------------- - ---------------------- + ---------------------- + ----------------------
22 22 22 22
$$- \frac{\sqrt{11} \log{\left(\sqrt{11} + 5 \right)}}{22} - \frac{\sqrt{11} \log{\left(4 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(5 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(\sqrt{11} + 4 \right)}}{22}$$
-sqrt(11)*log(4 - sqrt(11))/22 - sqrt(11)*log(5 + sqrt(11))/22 + sqrt(11)*log(4 + sqrt(11))/22 + sqrt(11)*log(5 - sqrt(11))/22
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.