Sr Examen
Integral de (3x+1)/(x^2-4x-2) dx
Solución
Ha introducido
[src]
1 / | | 3*x + 1 | ------------ dx | 2 | x - 4*x - 2 | / 0
$$\int\limits_{0}^{1} \frac{3 x + 1}{\left(x^{2} - 4 x\right) - 2}\, dx$$
Integral((3*x + 1)/(x^2 - 4*x - 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 6 *(-2 + x)| |
||-\/ 6 *acoth|--------------| |
/ || \ 6 / 2 |
| ||----------------------------- for (-2 + x) > 6| / 2 \
| 3*x + 1 || 6 | 3*log\-2 + x - 4*x/
| ------------ dx = C + 7*|< | + --------------------
| 2 || / ___ \ | 2
| x - 4*x - 2 || ___ |\/ 6 *(-2 + x)| |
| ||-\/ 6 *atanh|--------------| |
/ || \ 6 / 2 |
||----------------------------- for (-2 + x) < 6|
\\ 6 /
$$\int \frac{3 x + 1}{\left(x^{2} - 4 x\right) - 2}\, dx = C + 7 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} < 6 \end{cases}\right) + \frac{3 \log{\left(x^{2} - 4 x - 2 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ |3 7*\/ 6 | / ___\ |3 7*\/ 6 | / / ___\\ |3 7*\/ 6 | / ___\ |3 7*\/ 6 | / / ___\\ |- - -------|*log\-1 + \/ 6 / + |- + -------|*\pi*I + log\1 + \/ 6 // - |- - -------|*log\-2 + \/ 6 / - |- + -------|*\pi*I + log\2 + \/ 6 // \2 12 / \2 12 / \2 12 / \2 12 /
$$\left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-2 + \sqrt{6} \right)} - \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right)$$
=
=
/ ___\ / ___\ / ___\ / ___\ |3 7*\/ 6 | / ___\ |3 7*\/ 6 | / / ___\\ |3 7*\/ 6 | / ___\ |3 7*\/ 6 | / / ___\\ |- - -------|*log\-1 + \/ 6 / + |- + -------|*\pi*I + log\1 + \/ 6 // - |- - -------|*log\-2 + \/ 6 / - |- + -------|*\pi*I + log\2 + \/ 6 // \2 12 / \2 12 / \2 12 / \2 12 /
$$\left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-2 + \sqrt{6} \right)} - \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right)$$
(3/2 - 7*sqrt(6)/12)*log(-1 + sqrt(6)) + (3/2 + 7*sqrt(6)/12)*(pi*i + log(1 + sqrt(6))) - (3/2 - 7*sqrt(6)/12)*log(-2 + sqrt(6)) - (3/2 + 7*sqrt(6)/12)*(pi*i + log(2 + sqrt(6)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.