Sr Examen
Integral de dx/(7-x^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 2 | 7 - x | / 0
$$\int\limits_{0}^{1} \frac{1}{7 - x^{2}}\, dx$$
Integral(1/(7 - x^2), (x, 0, 1))
Solución detallada
-
Añadimos la constante de integración:
PieceweseRule(subfunctions=[(ArctanRule(a=1, b=-1, c=7, context=1/(7 - x**2), symbol=x), False), (ArccothRule(a=1, b=-1, c=7, context=1/(7 - x**2), symbol=x), x**2 > 7), (ArctanhRule(a=1, b=-1, c=7, context=1/(7 - x**2), symbol=x), x**2 < 7)], context=1/(7 - x**2), symbol=x)
Respuesta:
Respuesta (Indefinida)
[src]
// / ___\ \
|| ___ |x*\/ 7 | |
||\/ 7 *acoth|-------| |
/ || \ 7 / 2 |
| ||-------------------- for x > 7|
| 1 || 7 |
| ------ dx = C + |< |
| 2 || / ___\ |
| 7 - x || ___ |x*\/ 7 | |
| ||\/ 7 *atanh|-------| |
/ || \ 7 / 2 |
||-------------------- for x < 7|
\\ 7 /
$$\int \frac{1}{7 - x^{2}}\, dx = C + \begin{cases} \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{\sqrt{7} x}{7} \right)}}{7} & \text{for}\: x^{2} > 7 \\\frac{\sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7} x}{7} \right)}}{7} & \text{for}\: x^{2} < 7 \end{cases}$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 7 *\pi*I + log\-1 + \/ 7 // \/ 7 *log\\/ 7 / \/ 7 *\pi*I + log\\/ 7 // \/ 7 *log\1 + \/ 7 /
- ------------------------------ - ---------------- + ------------------------- + --------------------
14 14 14 14
$$- \frac{\sqrt{7} \log{\left(\sqrt{7} \right)}}{14} + \frac{\sqrt{7} \log{\left(1 + \sqrt{7} \right)}}{14} - \frac{\sqrt{7} \left(\log{\left(-1 + \sqrt{7} \right)} + i \pi\right)}{14} + \frac{\sqrt{7} \left(\log{\left(\sqrt{7} \right)} + i \pi\right)}{14}$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 7 *\pi*I + log\-1 + \/ 7 // \/ 7 *log\\/ 7 / \/ 7 *\pi*I + log\\/ 7 // \/ 7 *log\1 + \/ 7 /
- ------------------------------ - ---------------- + ------------------------- + --------------------
14 14 14 14
$$- \frac{\sqrt{7} \log{\left(\sqrt{7} \right)}}{14} + \frac{\sqrt{7} \log{\left(1 + \sqrt{7} \right)}}{14} - \frac{\sqrt{7} \left(\log{\left(-1 + \sqrt{7} \right)} + i \pi\right)}{14} + \frac{\sqrt{7} \left(\log{\left(\sqrt{7} \right)} + i \pi\right)}{14}$$
-sqrt(7)*(pi*i + log(-1 + sqrt(7)))/14 - sqrt(7)*log(sqrt(7))/14 + sqrt(7)*(pi*i + log(sqrt(7)))/14 + sqrt(7)*log(1 + sqrt(7))/14
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.