Sr Examen
Integral de (3*x+10)/(x^2-8*x+10) dx
Solución
Ha introducido
[src]
1 / | | 3*x + 10 | ------------- dx | 2 | x - 8*x + 10 | / 0
$$\int\limits_{0}^{1} \frac{3 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx$$
Integral((3*x + 10)/(x^2 - 8*x + 10), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 6 *(-4 + x)| |
||-\/ 6 *acoth|--------------| |
/ || \ 6 / 2 |
| ||----------------------------- for (-4 + x) > 6| / 2 \
| 3*x + 10 || 6 | 3*log\10 + x - 8*x/
| ------------- dx = C + 22*|< | + --------------------
| 2 || / ___ \ | 2
| x - 8*x + 10 || ___ |\/ 6 *(-4 + x)| |
| ||-\/ 6 *atanh|--------------| |
/ || \ 6 / 2 |
||----------------------------- for (-4 + x) < 6|
\\ 6 /
$$\int \frac{3 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx = C + 22 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 4\right)}{6} \right)}}{6} & \text{for}\: \left(x - 4\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 4\right)}{6} \right)}}{6} & \text{for}\: \left(x - 4\right)^{2} < 6 \end{cases}\right) + \frac{3 \log{\left(x^{2} - 8 x + 10 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ |3 11*\/ 6 | / / ___\\ |3 11*\/ 6 | / / ___\\ |3 11*\/ 6 | / / ___\\ |3 11*\/ 6 | / / ___\\ |- - --------|*\pi*I + log\3 - \/ 6 // + |- + --------|*\pi*I + log\3 + \/ 6 // - |- - --------|*\pi*I + log\4 - \/ 6 // - |- + --------|*\pi*I + log\4 + \/ 6 // \2 6 / \2 6 / \2 6 / \2 6 /
$$- \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)$$
=
=
/ ___\ / ___\ / ___\ / ___\ |3 11*\/ 6 | / / ___\\ |3 11*\/ 6 | / / ___\\ |3 11*\/ 6 | / / ___\\ |3 11*\/ 6 | / / ___\\ |- - --------|*\pi*I + log\3 - \/ 6 // + |- + --------|*\pi*I + log\3 + \/ 6 // - |- - --------|*\pi*I + log\4 - \/ 6 // - |- + --------|*\pi*I + log\4 + \/ 6 // \2 6 / \2 6 / \2 6 / \2 6 /
$$- \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)$$
(3/2 - 11*sqrt(6)/6)*(pi*i + log(3 - sqrt(6))) + (3/2 + 11*sqrt(6)/6)*(pi*i + log(3 + sqrt(6))) - (3/2 - 11*sqrt(6)/6)*(pi*i + log(4 - sqrt(6))) - (3/2 + 11*sqrt(6)/6)*(pi*i + log(4 + sqrt(6)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.