Sr Examen
Integral de (x+1)/(2x^2+3x-4) dx
Solución
Ha introducido
[src]
0 / | | x + 1 | -------------- dx | 2 | 2*x + 3*x - 4 | / 0
$$\int\limits_{0}^{0} \frac{x + 1}{\left(2 x^{2} + 3 x\right) - 4}\, dx$$
Integral((x + 1)/(2*x^2 + 3*x - 4), (x, 0, 0))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |4*\/ 41 *(3/4 + x)| |
||-\/ 41 *acoth|------------------| |
/ || \ 41 / 2 41|
| ||---------------------------------- for (3/4 + x) > --| / 2 \
| x + 1 || 164 16| log\-4 + 2*x + 3*x/
| -------------- dx = C + 2*|< | + --------------------
| 2 || / ____ \ | 4
| 2*x + 3*x - 4 || ____ |4*\/ 41 *(3/4 + x)| |
| ||-\/ 41 *atanh|------------------| |
/ || \ 41 / 2 41|
||---------------------------------- for (3/4 + x) < --|
\\ 164 16/
$$\int \frac{x + 1}{\left(2 x^{2} + 3 x\right) - 4}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{41} \operatorname{acoth}{\left(\frac{4 \sqrt{41} \left(x + \frac{3}{4}\right)}{41} \right)}}{164} & \text{for}\: \left(x + \frac{3}{4}\right)^{2} > \frac{41}{16} \\- \frac{\sqrt{41} \operatorname{atanh}{\left(\frac{4 \sqrt{41} \left(x + \frac{3}{4}\right)}{41} \right)}}{164} & \text{for}\: \left(x + \frac{3}{4}\right)^{2} < \frac{41}{16} \end{cases}\right) + \frac{\log{\left(2 x^{2} + 3 x - 4 \right)}}{4}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.