Sr Examen
Integral de 1/(2*x^2+6*x+3) dx
Solución
Ha introducido
[src]
oo / | | 1 | -------------- dx | 2 | 2*x + 6*x + 3 | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\left(2 x^{2} + 6 x\right) + 3}\, dx$$
Integral(1/(2*x^2 + 6*x + 3), (x, 2, oo))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |2*\/ 3 *(3/2 + x)| |
||-\/ 3 *acoth|-----------------| |
/ || \ 3 / 2 |
| ||-------------------------------- for (3/2 + x) > 3/4|
| 1 || 6 |
| -------------- dx = C + 2*|< |
| 2 || / ___ \ |
| 2*x + 6*x + 3 || ___ |2*\/ 3 *(3/2 + x)| |
| ||-\/ 3 *atanh|-----------------| |
/ || \ 3 / 2 |
||-------------------------------- for (3/2 + x) < 3/4|
\\ 6 /
$$\int \frac{1}{\left(2 x^{2} + 6 x\right) + 3}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3} \left(x + \frac{3}{2}\right)}{3} \right)}}{6} & \text{for}\: \left(x + \frac{3}{2}\right)^{2} > \frac{3}{4} \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{2 \sqrt{3} \left(x + \frac{3}{2}\right)}{3} \right)}}{6} & \text{for}\: \left(x + \frac{3}{2}\right)^{2} < \frac{3}{4} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |7 \/ 3 | ___ |7 \/ 3 |
\/ 3 *log|- - -----| \/ 3 *log|- + -----|
\2 2 / \2 2 /
- -------------------- + --------------------
6 6
$$- \frac{\sqrt{3} \log{\left(\frac{7}{2} - \frac{\sqrt{3}}{2} \right)}}{6} + \frac{\sqrt{3} \log{\left(\frac{\sqrt{3}}{2} + \frac{7}{2} \right)}}{6}$$
=
=
/ ___\ / ___\
___ |7 \/ 3 | ___ |7 \/ 3 |
\/ 3 *log|- - -----| \/ 3 *log|- + -----|
\2 2 / \2 2 /
- -------------------- + --------------------
6 6
$$- \frac{\sqrt{3} \log{\left(\frac{7}{2} - \frac{\sqrt{3}}{2} \right)}}{6} + \frac{\sqrt{3} \log{\left(\frac{\sqrt{3}}{2} + \frac{7}{2} \right)}}{6}$$
-sqrt(3)*log(7/2 - sqrt(3)/2)/6 + sqrt(3)*log(7/2 + sqrt(3)/2)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.