Sr Examen
Integral de (2x-10)/(√1+x-x^2) dx
Solución
Ha introducido
[src]
1 / | | 2*x - 10 | -------------- dx | ___ 2 | \/ 1 + x - x | / 0
$$\int\limits_{0}^{1} \frac{2 x - 10}{- x^{2} + \left(x + \sqrt{1}\right)}\, dx$$
Integral((2*x - 10)/(sqrt(1) + x - x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |2*\/ 5 *(-1/2 + x)| |
||-\/ 5 *acoth|------------------| |
/ || \ 5 / 2 |
| ||--------------------------------- for (-1/2 + x) > 5/4|
| 2*x - 10 / 2 \ || 10 |
| -------------- dx = C - log\-1 + x - x/ + 36*|< |
| ___ 2 || / ___ \ |
| \/ 1 + x - x || ___ |2*\/ 5 *(-1/2 + x)| |
| ||-\/ 5 *atanh|------------------| |
/ || \ 5 / 2 |
||--------------------------------- for (-1/2 + x) < 5/4|
\\ 10 /
$$\int \frac{2 x - 10}{- x^{2} + \left(x + \sqrt{1}\right)}\, dx = C + 36 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(x - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(x - \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(x - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(x - \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) - \log{\left(x^{2} - x - 1 \right)}$$
Gráfica
Respuesta
[src]
/ ___\ / / ___\\ / ___\ / ___\ / ___\ / / ___\\ / ___\ / ___\ | 9*\/ 5 | | |1 \/ 5 || | 9*\/ 5 | | 1 \/ 5 | | 9*\/ 5 | | | 1 \/ 5 || | 9*\/ 5 | |1 \/ 5 | |1 - -------|*|pi*I + log|- + -----|| + |1 + -------|*log|- - + -----| - |1 - -------|*|pi*I + log|- - + -----|| - |1 + -------|*log|- + -----| \ 5 / \ \2 2 // \ 5 / \ 2 2 / \ 5 / \ \ 2 2 // \ 5 / \2 2 /
$$\left(1 + \frac{9 \sqrt{5}}{5}\right) \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - \left(1 + \frac{9 \sqrt{5}}{5}\right) \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + \left(1 - \frac{9 \sqrt{5}}{5}\right) \left(\log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right) - \left(1 - \frac{9 \sqrt{5}}{5}\right) \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)$$
=
=
/ ___\ / / ___\\ / ___\ / ___\ / ___\ / / ___\\ / ___\ / ___\ | 9*\/ 5 | | |1 \/ 5 || | 9*\/ 5 | | 1 \/ 5 | | 9*\/ 5 | | | 1 \/ 5 || | 9*\/ 5 | |1 \/ 5 | |1 - -------|*|pi*I + log|- + -----|| + |1 + -------|*log|- - + -----| - |1 - -------|*|pi*I + log|- - + -----|| - |1 + -------|*log|- + -----| \ 5 / \ \2 2 // \ 5 / \ 2 2 / \ 5 / \ \ 2 2 // \ 5 / \2 2 /
$$\left(1 + \frac{9 \sqrt{5}}{5}\right) \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - \left(1 + \frac{9 \sqrt{5}}{5}\right) \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + \left(1 - \frac{9 \sqrt{5}}{5}\right) \left(\log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right) - \left(1 - \frac{9 \sqrt{5}}{5}\right) \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)$$
(1 - 9*sqrt(5)/5)*(pi*i + log(1/2 + sqrt(5)/2)) + (1 + 9*sqrt(5)/5)*log(-1/2 + sqrt(5)/2) - (1 - 9*sqrt(5)/5)*(pi*i + log(-1/2 + sqrt(5)/2)) - (1 + 9*sqrt(5)/5)*log(1/2 + sqrt(5)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.