Sr Examen
Integral de (4*x+10)/(x^2-8*x+10) dx
Solución
Ha introducido
[src]
1 / | | 4*x + 10 | ------------- dx | 2 | x - 8*x + 10 | / 0
$$\int\limits_{0}^{1} \frac{4 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx$$
Integral((4*x + 10)/(x^2 - 8*x + 10), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 6 *(-4 + x)| |
||-\/ 6 *acoth|--------------| |
/ || \ 6 / 2 |
| ||----------------------------- for (-4 + x) > 6|
| 4*x + 10 / 2 \ || 6 |
| ------------- dx = C + 2*log\10 + x - 8*x/ + 26*|< |
| 2 || / ___ \ |
| x - 8*x + 10 || ___ |\/ 6 *(-4 + x)| |
| ||-\/ 6 *atanh|--------------| |
/ || \ 6 / 2 |
||----------------------------- for (-4 + x) < 6|
\\ 6 /
$$\int \frac{4 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx = C + 26 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 4\right)}{6} \right)}}{6} & \text{for}\: \left(x - 4\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 4\right)}{6} \right)}}{6} & \text{for}\: \left(x - 4\right)^{2} < 6 \end{cases}\right) + 2 \log{\left(x^{2} - 8 x + 10 \right)}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ | 13*\/ 6 | / / ___\\ | 13*\/ 6 | / / ___\\ | 13*\/ 6 | / / ___\\ | 13*\/ 6 | / / ___\\ |2 - --------|*\pi*I + log\3 - \/ 6 // + |2 + --------|*\pi*I + log\3 + \/ 6 // - |2 - --------|*\pi*I + log\4 - \/ 6 // - |2 + --------|*\pi*I + log\4 + \/ 6 // \ 6 / \ 6 / \ 6 / \ 6 /
$$- \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)$$
=
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/ ___\ / ___\ / ___\ / ___\ | 13*\/ 6 | / / ___\\ | 13*\/ 6 | / / ___\\ | 13*\/ 6 | / / ___\\ | 13*\/ 6 | / / ___\\ |2 - --------|*\pi*I + log\3 - \/ 6 // + |2 + --------|*\pi*I + log\3 + \/ 6 // - |2 - --------|*\pi*I + log\4 - \/ 6 // - |2 + --------|*\pi*I + log\4 + \/ 6 // \ 6 / \ 6 / \ 6 / \ 6 /
$$- \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)$$
(2 - 13*sqrt(6)/6)*(pi*i + log(3 - sqrt(6))) + (2 + 13*sqrt(6)/6)*(pi*i + log(3 + sqrt(6))) - (2 - 13*sqrt(6)/6)*(pi*i + log(4 - sqrt(6))) - (2 + 13*sqrt(6)/6)*(pi*i + log(4 + sqrt(6)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.