Sr Examen
Integral de (x-3)/(4x^2+2x-3) dx
Solución
Ha introducido
[src]
1 / | | x - 3 | -------------- dx | 2 | 4*x + 2*x - 3 | / 0
$$\int\limits_{0}^{1} \frac{x - 3}{\left(4 x^{2} + 2 x\right) - 3}\, dx$$
Integral((x - 3)/(4*x^2 + 2*x - 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |4*\/ 13 *(1/4 + x)| |
||-\/ 13 *acoth|------------------| |
/ || \ 13 / 2 13|
| ||---------------------------------- for (1/4 + x) > --| / 2\
| x - 3 || 52 16| log\-3 + 2*x + 4*x /
| -------------- dx = C - 13*|< | + --------------------
| 2 || / ____ \ | 8
| 4*x + 2*x - 3 || ____ |4*\/ 13 *(1/4 + x)| |
| ||-\/ 13 *atanh|------------------| |
/ || \ 13 / 2 13|
||---------------------------------- for (1/4 + x) < --|
\\ 52 16/
$$\int \frac{x - 3}{\left(4 x^{2} + 2 x\right) - 3}\, dx = C - 13 \left(\begin{cases} - \frac{\sqrt{13} \operatorname{acoth}{\left(\frac{4 \sqrt{13} \left(x + \frac{1}{4}\right)}{13} \right)}}{52} & \text{for}\: \left(x + \frac{1}{4}\right)^{2} > \frac{13}{16} \\- \frac{\sqrt{13} \operatorname{atanh}{\left(\frac{4 \sqrt{13} \left(x + \frac{1}{4}\right)}{13} \right)}}{52} & \text{for}\: \left(x + \frac{1}{4}\right)^{2} < \frac{13}{16} \end{cases}\right) + \frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.