Sr Examen
Integral de x^2/(7-6*x^2) dx
Solución
Ha introducido
[src]
1 / | | 2 | x | -------- dx | 2 | 7 - 6*x | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{7 - 6 x^{2}}\, dx$$
Integral(x^2/(7 - 6*x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____\ \
|| ____ |x*\/ 42 | |
||-\/ 42 *acoth|--------| |
|| \ 7 / 2 |
||------------------------ for x > 7/6|
|| 42 |
7*|< |
|| / ____\ |
|| ____ |x*\/ 42 | |
/ ||-\/ 42 *atanh|--------| |
| || \ 7 / 2 |
| 2 ||------------------------ for x < 7/6|
| x \\ 42 / x
| -------- dx = C - ------------------------------------------- - -
| 2 6 6
| 7 - 6*x
|
/
$$\int \frac{x^{2}}{7 - 6 x^{2}}\, dx = C - \frac{x}{6} - \frac{7 \left(\begin{cases} - \frac{\sqrt{42} \operatorname{acoth}{\left(\frac{\sqrt{42} x}{7} \right)}}{42} & \text{for}\: x^{2} > \frac{7}{6} \\- \frac{\sqrt{42} \operatorname{atanh}{\left(\frac{\sqrt{42} x}{7} \right)}}{42} & \text{for}\: x^{2} < \frac{7}{6} \end{cases}\right)}{6}$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | \/ 42 || ____ |\/ 42 | ____ | |\/ 42 || ____ | \/ 42 |
\/ 42 *|pi*I + log|-1 + ------|| \/ 42 *log|------| \/ 42 *|pi*I + log|------|| \/ 42 *log|1 + ------|
1 \ \ 6 // \ 6 / \ \ 6 // \ 6 /
- - - -------------------------------- - ------------------ + --------------------------- + ----------------------
6 72 72 72 72
$$- \frac{1}{6} - \frac{\sqrt{42} \log{\left(\frac{\sqrt{42}}{6} \right)}}{72} + \frac{\sqrt{42} \log{\left(1 + \frac{\sqrt{42}}{6} \right)}}{72} - \frac{\sqrt{42} \left(\log{\left(-1 + \frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72} + \frac{\sqrt{42} \left(\log{\left(\frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | \/ 42 || ____ |\/ 42 | ____ | |\/ 42 || ____ | \/ 42 |
\/ 42 *|pi*I + log|-1 + ------|| \/ 42 *log|------| \/ 42 *|pi*I + log|------|| \/ 42 *log|1 + ------|
1 \ \ 6 // \ 6 / \ \ 6 // \ 6 /
- - - -------------------------------- - ------------------ + --------------------------- + ----------------------
6 72 72 72 72
$$- \frac{1}{6} - \frac{\sqrt{42} \log{\left(\frac{\sqrt{42}}{6} \right)}}{72} + \frac{\sqrt{42} \log{\left(1 + \frac{\sqrt{42}}{6} \right)}}{72} - \frac{\sqrt{42} \left(\log{\left(-1 + \frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72} + \frac{\sqrt{42} \left(\log{\left(\frac{\sqrt{42}}{6} \right)} + i \pi\right)}{72}$$
-1/6 - sqrt(42)*(pi*i + log(-1 + sqrt(42)/6))/72 - sqrt(42)*log(sqrt(42)/6)/72 + sqrt(42)*(pi*i + log(sqrt(42)/6))/72 + sqrt(42)*log(1 + sqrt(42)/6)/72
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.