Sr Examen
Integral de (3*x+2)/(x^2+8*x-3) dx
Solución
Ha introducido
[src]
1 / | | 3*x + 2 | ------------ dx | 2 | x + 8*x - 3 | / 0
$$\int\limits_{0}^{1} \frac{3 x + 2}{\left(x^{2} + 8 x\right) - 3}\, dx$$
Integral((3*x + 2)/(x^2 + 8*x - 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |\/ 19 *(4 + x)| |
||-\/ 19 *acoth|--------------| |
/ || \ 19 / 2 |
| ||------------------------------ for (4 + x) > 19| / 2 \
| 3*x + 2 || 19 | 3*log\-3 + x + 8*x/
| ------------ dx = C - 10*|< | + --------------------
| 2 || / ____ \ | 2
| x + 8*x - 3 || ____ |\/ 19 *(4 + x)| |
| ||-\/ 19 *atanh|--------------| |
/ || \ 19 / 2 |
||------------------------------ for (4 + x) < 19|
\\ 19 /
$$\int \frac{3 x + 2}{\left(x^{2} + 8 x\right) - 3}\, dx = C - 10 \left(\begin{cases} - \frac{\sqrt{19} \operatorname{acoth}{\left(\frac{\sqrt{19} \left(x + 4\right)}{19} \right)}}{19} & \text{for}\: \left(x + 4\right)^{2} > 19 \\- \frac{\sqrt{19} \operatorname{atanh}{\left(\frac{\sqrt{19} \left(x + 4\right)}{19} \right)}}{19} & \text{for}\: \left(x + 4\right)^{2} < 19 \end{cases}\right) + \frac{3 \log{\left(x^{2} + 8 x - 3 \right)}}{2}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.