Sr Examen
Integral de (5-2x)/(x^2-8x-3) dx
Solución
Ha introducido
[src]
1 / | | 5 - 2*x | ------------ dx | 2 | x - 8*x - 3 | / 0
$$\int\limits_{0}^{1} \frac{5 - 2 x}{\left(x^{2} - 8 x\right) - 3}\, dx$$
Integral((5 - 2*x)/(x^2 - 8*x - 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |\/ 19 *(-4 + x)| |
||-\/ 19 *acoth|---------------| |
/ || \ 19 / 2 |
| ||------------------------------- for (-4 + x) > 19|
| 5 - 2*x / 2 \ || 19 |
| ------------ dx = C - log\-3 + x - 8*x/ - 3*|< |
| 2 || / ____ \ |
| x - 8*x - 3 || ____ |\/ 19 *(-4 + x)| |
| ||-\/ 19 *atanh|---------------| |
/ || \ 19 / 2 |
||------------------------------- for (-4 + x) < 19|
\\ 19 /
$$\int \frac{5 - 2 x}{\left(x^{2} - 8 x\right) - 3}\, dx = C - 3 \left(\begin{cases} - \frac{\sqrt{19} \operatorname{acoth}{\left(\frac{\sqrt{19} \left(x - 4\right)}{19} \right)}}{19} & \text{for}\: \left(x - 4\right)^{2} > 19 \\- \frac{\sqrt{19} \operatorname{atanh}{\left(\frac{\sqrt{19} \left(x - 4\right)}{19} \right)}}{19} & \text{for}\: \left(x - 4\right)^{2} < 19 \end{cases}\right) - \log{\left(x^{2} - 8 x - 3 \right)}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\ / ____\ / ____\ | 3*\/ 19 | / ____\ | 3*\/ 19 | / / ____\\ | 3*\/ 19 | / ____\ | 3*\/ 19 | / / ____\\ |1 - --------|*log\-4 + \/ 19 / + |1 + --------|*\pi*I + log\4 + \/ 19 // - |1 - --------|*log\-3 + \/ 19 / - |1 + --------|*\pi*I + log\3 + \/ 19 // \ 38 / \ 38 / \ 38 / \ 38 /
$$\left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-4 + \sqrt{19} \right)} - \left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-3 + \sqrt{19} \right)} - \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(3 + \sqrt{19} \right)} + i \pi\right) + \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(4 + \sqrt{19} \right)} + i \pi\right)$$
=
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/ ____\ / ____\ / ____\ / ____\ | 3*\/ 19 | / ____\ | 3*\/ 19 | / / ____\\ | 3*\/ 19 | / ____\ | 3*\/ 19 | / / ____\\ |1 - --------|*log\-4 + \/ 19 / + |1 + --------|*\pi*I + log\4 + \/ 19 // - |1 - --------|*log\-3 + \/ 19 / - |1 + --------|*\pi*I + log\3 + \/ 19 // \ 38 / \ 38 / \ 38 / \ 38 /
$$\left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-4 + \sqrt{19} \right)} - \left(1 - \frac{3 \sqrt{19}}{38}\right) \log{\left(-3 + \sqrt{19} \right)} - \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(3 + \sqrt{19} \right)} + i \pi\right) + \left(\frac{3 \sqrt{19}}{38} + 1\right) \left(\log{\left(4 + \sqrt{19} \right)} + i \pi\right)$$
(1 - 3*sqrt(19)/38)*log(-4 + sqrt(19)) + (1 + 3*sqrt(19)/38)*(pi*i + log(4 + sqrt(19))) - (1 - 3*sqrt(19)/38)*log(-3 + sqrt(19)) - (1 + 3*sqrt(19)/38)*(pi*i + log(3 + sqrt(19)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.