Sr Examen
Integral de (4x-3)/(x^2+5x-9) dx
Solución
Ha introducido
[src]
1 / | | 4*x - 3 | ------------ dx | 2 | x + 5*x - 9 | / 0
$$\int\limits_{0}^{1} \frac{4 x - 3}{\left(x^{2} + 5 x\right) - 9}\, dx$$
Integral((4*x - 3)/(x^2 + 5*x - 9), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 61 *(5/2 + x)| |
||-\/ 61 *acoth|------------------| |
/ || \ 61 / 2 |
| ||---------------------------------- for (5/2 + x) > 61/4|
| 4*x - 3 || 122 | / 2 \
| ------------ dx = C - 52*|< | + 2*log\-9 + x + 5*x/
| 2 || / ____ \ |
| x + 5*x - 9 || ____ |2*\/ 61 *(5/2 + x)| |
| ||-\/ 61 *atanh|------------------| |
/ || \ 61 / 2 |
||---------------------------------- for (5/2 + x) < 61/4|
\\ 122 /
$$\int \frac{4 x - 3}{\left(x^{2} + 5 x\right) - 9}\, dx = C - 52 \left(\begin{cases} - \frac{\sqrt{61} \operatorname{acoth}{\left(\frac{2 \sqrt{61} \left(x + \frac{5}{2}\right)}{61} \right)}}{122} & \text{for}\: \left(x + \frac{5}{2}\right)^{2} > \frac{61}{4} \\- \frac{\sqrt{61} \operatorname{atanh}{\left(\frac{2 \sqrt{61} \left(x + \frac{5}{2}\right)}{61} \right)}}{122} & \text{for}\: \left(x + \frac{5}{2}\right)^{2} < \frac{61}{4} \end{cases}\right) + 2 \log{\left(x^{2} + 5 x - 9 \right)}$$
Gráfica
Respuesta
[src]
/ ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ | 13*\/ 61 | | | 7 \/ 61 || | 13*\/ 61 | |7 \/ 61 | | 13*\/ 61 | | | 5 \/ 61 || | 13*\/ 61 | |5 \/ 61 | |2 - ---------|*|pi*I + log|- - + ------|| + |2 + ---------|*log|- + ------| - |2 - ---------|*|pi*I + log|- - + ------|| - |2 + ---------|*log|- + ------| \ 61 / \ \ 2 2 // \ 61 / \2 2 / \ 61 / \ \ 2 2 // \ 61 / \2 2 /
$$- \left(\frac{13 \sqrt{61}}{61} + 2\right) \log{\left(\frac{5}{2} + \frac{\sqrt{61}}{2} \right)} + \left(\frac{13 \sqrt{61}}{61} + 2\right) \log{\left(\frac{7}{2} + \frac{\sqrt{61}}{2} \right)} - \left(2 - \frac{13 \sqrt{61}}{61}\right) \left(\log{\left(- \frac{5}{2} + \frac{\sqrt{61}}{2} \right)} + i \pi\right) + \left(2 - \frac{13 \sqrt{61}}{61}\right) \left(\log{\left(- \frac{7}{2} + \frac{\sqrt{61}}{2} \right)} + i \pi\right)$$
=
=
/ ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ | 13*\/ 61 | | | 7 \/ 61 || | 13*\/ 61 | |7 \/ 61 | | 13*\/ 61 | | | 5 \/ 61 || | 13*\/ 61 | |5 \/ 61 | |2 - ---------|*|pi*I + log|- - + ------|| + |2 + ---------|*log|- + ------| - |2 - ---------|*|pi*I + log|- - + ------|| - |2 + ---------|*log|- + ------| \ 61 / \ \ 2 2 // \ 61 / \2 2 / \ 61 / \ \ 2 2 // \ 61 / \2 2 /
$$- \left(\frac{13 \sqrt{61}}{61} + 2\right) \log{\left(\frac{5}{2} + \frac{\sqrt{61}}{2} \right)} + \left(\frac{13 \sqrt{61}}{61} + 2\right) \log{\left(\frac{7}{2} + \frac{\sqrt{61}}{2} \right)} - \left(2 - \frac{13 \sqrt{61}}{61}\right) \left(\log{\left(- \frac{5}{2} + \frac{\sqrt{61}}{2} \right)} + i \pi\right) + \left(2 - \frac{13 \sqrt{61}}{61}\right) \left(\log{\left(- \frac{7}{2} + \frac{\sqrt{61}}{2} \right)} + i \pi\right)$$
(2 - 13*sqrt(61)/61)*(pi*i + log(-7/2 + sqrt(61)/2)) + (2 + 13*sqrt(61)/61)*log(7/2 + sqrt(61)/2) - (2 - 13*sqrt(61)/61)*(pi*i + log(-5/2 + sqrt(61)/2)) - (2 + 13*sqrt(61)/61)*log(5/2 + sqrt(61)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.