Sr Examen
Integral de 2/(-3*x*x+10*x+1) dx
Solución
Ha introducido
[src]
1 / | | 2 | ----------------- dx | -3*x*x + 10*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{2}{\left(- 3 x x + 10 x\right) + 1}\, dx$$
Integral(2/((-3*x)*x + 10*x + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |3*\/ 7 *(-5/3 + x)| |
||-\/ 7 *acoth|------------------| |
/ || \ 14 / 2 |
| ||--------------------------------- for (-5/3 + x) > 28/9|
| 2 || 42 |
| ----------------- dx = C - 6*|< |
| -3*x*x + 10*x + 1 || / ___ \ |
| || ___ |3*\/ 7 *(-5/3 + x)| |
/ ||-\/ 7 *atanh|------------------| |
|| \ 14 / 2 |
||--------------------------------- for (-5/3 + x) < 28/9|
\\ 42 /
$$\int \frac{2}{\left(- 3 x x + 10 x\right) + 1}\, dx = C - 6 \left(\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{3 \sqrt{7} \left(x - \frac{5}{3}\right)}{14} \right)}}{42} & \text{for}\: \left(x - \frac{5}{3}\right)^{2} > \frac{28}{9} \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{3 \sqrt{7} \left(x - \frac{5}{3}\right)}{14} \right)}}{42} & \text{for}\: \left(x - \frac{5}{3}\right)^{2} < \frac{28}{9} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ / ___\\ / ___\ / / ___\\ / ___\
___ | |2 2*\/ 7 || ___ | 5 2*\/ 7 | ___ | |5 2*\/ 7 || ___ | 2 2*\/ 7 |
\/ 7 *|pi*I + log|- + -------|| \/ 7 *log|- - + -------| \/ 7 *|pi*I + log|- + -------|| \/ 7 *log|- - + -------|
\ \3 3 // \ 3 3 / \ \3 3 // \ 3 3 /
- ------------------------------- - ------------------------ + ------------------------------- + ------------------------
14 14 14 14
$$\frac{\sqrt{7} \log{\left(- \frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \log{\left(- \frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \left(\log{\left(\frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14} + \frac{\sqrt{7} \left(\log{\left(\frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14}$$
=
=
/ / ___\\ / ___\ / / ___\\ / ___\
___ | |2 2*\/ 7 || ___ | 5 2*\/ 7 | ___ | |5 2*\/ 7 || ___ | 2 2*\/ 7 |
\/ 7 *|pi*I + log|- + -------|| \/ 7 *log|- - + -------| \/ 7 *|pi*I + log|- + -------|| \/ 7 *log|- - + -------|
\ \3 3 // \ 3 3 / \ \3 3 // \ 3 3 /
- ------------------------------- - ------------------------ + ------------------------------- + ------------------------
14 14 14 14
$$\frac{\sqrt{7} \log{\left(- \frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \log{\left(- \frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)}}{14} - \frac{\sqrt{7} \left(\log{\left(\frac{2}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14} + \frac{\sqrt{7} \left(\log{\left(\frac{5}{3} + \frac{2 \sqrt{7}}{3} \right)} + i \pi\right)}{14}$$
-sqrt(7)*(pi*i + log(2/3 + 2*sqrt(7)/3))/14 - sqrt(7)*log(-5/3 + 2*sqrt(7)/3)/14 + sqrt(7)*(pi*i + log(5/3 + 2*sqrt(7)/3))/14 + sqrt(7)*log(-2/3 + 2*sqrt(7)/3)/14
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.