Sr Examen
Integral de (4x-5)/(3-4x-5x^2) dx
Solución
Ha introducido
[src]
1 / | | 4*x - 5 | -------------- dx | 2 | 3 - 4*x - 5*x | / 0
$$\int\limits_{0}^{1} \frac{4 x - 5}{- 5 x^{2} + \left(3 - 4 x\right)}\, dx$$
Integral((4*x - 5)/(3 - 4*x - 5*x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |5*\/ 19 *(2/5 + x)| |
||-\/ 19 *acoth|------------------| |
/ || \ 19 / 2 19|
| ||---------------------------------- for (2/5 + x) > --| / 2\
| 4*x - 5 || 95 25| 2*log\-3 + 4*x + 5*x /
| -------------- dx = C + 33*|< | - ----------------------
| 2 || / ____ \ | 5
| 3 - 4*x - 5*x || ____ |5*\/ 19 *(2/5 + x)| |
| ||-\/ 19 *atanh|------------------| |
/ || \ 19 / 2 19|
||---------------------------------- for (2/5 + x) < --|
\\ 95 25/
$$\int \frac{4 x - 5}{- 5 x^{2} + \left(3 - 4 x\right)}\, dx = C + 33 \left(\begin{cases} - \frac{\sqrt{19} \operatorname{acoth}{\left(\frac{5 \sqrt{19} \left(x + \frac{2}{5}\right)}{19} \right)}}{95} & \text{for}\: \left(x + \frac{2}{5}\right)^{2} > \frac{19}{25} \\- \frac{\sqrt{19} \operatorname{atanh}{\left(\frac{5 \sqrt{19} \left(x + \frac{2}{5}\right)}{19} \right)}}{95} & \text{for}\: \left(x + \frac{2}{5}\right)^{2} < \frac{19}{25} \end{cases}\right) - \frac{2 \log{\left(5 x^{2} + 4 x - 3 \right)}}{5}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.