Sr Examen
Integral de dx/(x^2-6*x+6) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 2 | x - 6*x + 6 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 6 x\right) + 6}\, dx$$
Integral(1/(x^2 - 6*x + 6), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 3 *(-3 + x)| |
||-\/ 3 *acoth|--------------| |
/ || \ 3 / 2 |
| ||----------------------------- for (-3 + x) > 3|
| 1 || 3 |
| ------------ dx = C + |< |
| 2 || / ___ \ |
| x - 6*x + 6 || ___ |\/ 3 *(-3 + x)| |
| ||-\/ 3 *atanh|--------------| |
/ || \ 3 / 2 |
||----------------------------- for (-3 + x) < 3|
\\ 3 /
$$\int \frac{1}{\left(x^{2} - 6 x\right) + 6}\, dx = C + \begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \left(x - 3\right)}{3} \right)}}{3} & \text{for}\: \left(x - 3\right)^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \left(x - 3\right)}{3} \right)}}{3} & \text{for}\: \left(x - 3\right)^{2} < 3 \end{cases}$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / / ___\\ ___ / / ___\\ ___ / / ___\\
\/ 3 *\pi*I + log\2 - \/ 3 // \/ 3 *\pi*I + log\3 + \/ 3 // \/ 3 *\pi*I + log\2 + \/ 3 // \/ 3 *\pi*I + log\3 - \/ 3 //
- ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
6 6 6 6
$$- \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{3} \left(\log{\left(2 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(3 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 2 \right)} + i \pi\right)}{6}$$
=
=
___ / / ___\\ ___ / / ___\\ ___ / / ___\\ ___ / / ___\\
\/ 3 *\pi*I + log\2 - \/ 3 // \/ 3 *\pi*I + log\3 + \/ 3 // \/ 3 *\pi*I + log\2 + \/ 3 // \/ 3 *\pi*I + log\3 - \/ 3 //
- ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
6 6 6 6
$$- \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{3} \left(\log{\left(2 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(3 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 2 \right)} + i \pi\right)}{6}$$
-sqrt(3)*(pi*i + log(2 - sqrt(3)))/6 - sqrt(3)*(pi*i + log(3 + sqrt(3)))/6 + sqrt(3)*(pi*i + log(2 + sqrt(3)))/6 + sqrt(3)*(pi*i + log(3 - sqrt(3)))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.