Sr Examen
Integral de (1-x)/(-x^2-2*x+26) dx
Solución
Ha introducido
[src]
1 / | | 1 - x | --------------- dx | 2 | - x - 2*x + 26 | / 0
$$\int\limits_{0}^{1} \frac{1 - x}{\left(- x^{2} - 2 x\right) + 26}\, dx$$
Integral((1 - x)/(-x^2 - 2*x + 26), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 3 *(1 + x)| |
||-\/ 3 *acoth|-------------| |
/ || \ 9 / 2 |
| / 2 \ ||---------------------------- for (1 + x) > 27|
| 1 - x log\26 - x - 2*x/ || 9 |
| --------------- dx = C + ------------------ - 2*|< |
| 2 2 || / ___ \ |
| - x - 2*x + 26 || ___ |\/ 3 *(1 + x)| |
| ||-\/ 3 *atanh|-------------| |
/ || \ 9 / 2 |
||---------------------------- for (1 + x) < 27|
\\ 9 /
$$\int \frac{1 - x}{\left(- x^{2} - 2 x\right) + 26}\, dx = C - 2 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \left(x + 1\right)}{9} \right)}}{9} & \text{for}\: \left(x + 1\right)^{2} > 27 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \left(x + 1\right)}{9} \right)}}{9} & \text{for}\: \left(x + 1\right)^{2} < 27 \end{cases}\right) + \frac{\log{\left(- x^{2} - 2 x + 26 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ |1 \/ 3 | / / ___\\ |1 \/ 3 | / ___\ |1 \/ 3 | / / ___\\ |1 \/ 3 | / ___\ |- - -----|*\pi*I + log\-2 + 3*\/ 3 // + |- + -----|*log\2 + 3*\/ 3 / - |- - -----|*\pi*I + log\-1 + 3*\/ 3 // - |- + -----|*log\1 + 3*\/ 3 / \2 9 / \2 9 / \2 9 / \2 9 /
$$- \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(1 + 3 \sqrt{3} \right)} + \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(2 + 3 \sqrt{3} \right)} - \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-1 + 3 \sqrt{3} \right)} + i \pi\right) + \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-2 + 3 \sqrt{3} \right)} + i \pi\right)$$
=
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/ ___\ / ___\ / ___\ / ___\ |1 \/ 3 | / / ___\\ |1 \/ 3 | / ___\ |1 \/ 3 | / / ___\\ |1 \/ 3 | / ___\ |- - -----|*\pi*I + log\-2 + 3*\/ 3 // + |- + -----|*log\2 + 3*\/ 3 / - |- - -----|*\pi*I + log\-1 + 3*\/ 3 // - |- + -----|*log\1 + 3*\/ 3 / \2 9 / \2 9 / \2 9 / \2 9 /
$$- \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(1 + 3 \sqrt{3} \right)} + \left(\frac{\sqrt{3}}{9} + \frac{1}{2}\right) \log{\left(2 + 3 \sqrt{3} \right)} - \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-1 + 3 \sqrt{3} \right)} + i \pi\right) + \left(\frac{1}{2} - \frac{\sqrt{3}}{9}\right) \left(\log{\left(-2 + 3 \sqrt{3} \right)} + i \pi\right)$$
(1/2 - sqrt(3)/9)*(pi*i + log(-2 + 3*sqrt(3))) + (1/2 + sqrt(3)/9)*log(2 + 3*sqrt(3)) - (1/2 - sqrt(3)/9)*(pi*i + log(-1 + 3*sqrt(3))) - (1/2 + sqrt(3)/9)*log(1 + 3*sqrt(3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.