Sr Examen
Integral de (7x-2)/(x^2+5x-1) dx
Solución
Ha introducido
[src]
1 / | | 7*x - 2 | ------------ dx | 2 | x + 5*x - 1 | / 0
$$\int\limits_{0}^{1} \frac{7 x - 2}{\left(x^{2} + 5 x\right) - 1}\, dx$$
Integral((7*x - 2)/(x^2 + 5*x - 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |2*\/ 29 *(5/2 + x)| |
||-\/ 29 *acoth|------------------| |
/ || \ 29 / 2 |
| ||---------------------------------- for (5/2 + x) > 29/4| / 2 \
| 7*x - 2 || 58 | 7*log\-1 + x + 5*x/
| ------------ dx = C - 78*|< | + --------------------
| 2 || / ____ \ | 2
| x + 5*x - 1 || ____ |2*\/ 29 *(5/2 + x)| |
| ||-\/ 29 *atanh|------------------| |
/ || \ 29 / 2 |
||---------------------------------- for (5/2 + x) < 29/4|
\\ 58 /
$$\int \frac{7 x - 2}{\left(x^{2} + 5 x\right) - 1}\, dx = C - 78 \left(\begin{cases} - \frac{\sqrt{29} \operatorname{acoth}{\left(\frac{2 \sqrt{29} \left(x + \frac{5}{2}\right)}{29} \right)}}{58} & \text{for}\: \left(x + \frac{5}{2}\right)^{2} > \frac{29}{4} \\- \frac{\sqrt{29} \operatorname{atanh}{\left(\frac{2 \sqrt{29} \left(x + \frac{5}{2}\right)}{29} \right)}}{58} & \text{for}\: \left(x + \frac{5}{2}\right)^{2} < \frac{29}{4} \end{cases}\right) + \frac{7 \log{\left(x^{2} + 5 x - 1 \right)}}{2}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.