Sr Examen
Integral de 1/(x*sqrt(x^2-a^2)) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------------- dx | _________ | / 2 2 | x*\/ x - a | / 0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- a^{2} + x^{2}}}\, dx$$
Integral(1/(x*sqrt(x^2 - a^2)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// /a\ \
||I*acosh|-| | 2| |
|| \x/ |a | |
/ ||---------- for |--| > 1|
| || a | 2| |
| 1 || |x | |
| -------------- dx = C + |< |
| _________ || /a\ |
| / 2 2 ||-asin|-| |
| x*\/ x - a || \x/ |
| ||--------- otherwise |
/ || a |
\\ /
$$\int \frac{1}{x \sqrt{- a^{2} + x^{2}}}\, dx = C + \begin{cases} \frac{i \operatorname{acosh}{\left(\frac{a}{x} \right)}}{a} & \text{for}\: \left|{\frac{a^{2}}{x^{2}}}\right| > 1 \\- \frac{\operatorname{asin}{\left(\frac{a}{x} \right)}}{a} & \text{otherwise} \end{cases}$$
Respuesta
[src]
1 / | | / | 2| | | -I |a | | |------------------ for ---- > 1 | | _________ 2 | | / 2 x | | 2 / a | |x * / -1 + -- | | / 2 | | \/ x | < dx | | 1 | |----------------- otherwise | | ________ | | / 2 | | 2 / a | |x * / 1 - -- | | / 2 | | \/ x | \ | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i}{x^{2} \sqrt{\frac{a^{2}}{x^{2}} - 1}} & \text{for}\: \frac{\left|{a^{2}}\right|}{x^{2}} > 1 \\\frac{1}{x^{2} \sqrt{- \frac{a^{2}}{x^{2}} + 1}} & \text{otherwise} \end{cases}\, dx$$
=
=
1 / | | / | 2| | | -I |a | | |------------------ for ---- > 1 | | _________ 2 | | / 2 x | | 2 / a | |x * / -1 + -- | | / 2 | | \/ x | < dx | | 1 | |----------------- otherwise | | ________ | | / 2 | | 2 / a | |x * / 1 - -- | | / 2 | | \/ x | \ | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i}{x^{2} \sqrt{\frac{a^{2}}{x^{2}} - 1}} & \text{for}\: \frac{\left|{a^{2}}\right|}{x^{2}} > 1 \\\frac{1}{x^{2} \sqrt{- \frac{a^{2}}{x^{2}} + 1}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i/(x^2*sqrt(-1 + a^2/x^2)), |a^2|/x^2 > 1), (1/(x^2*sqrt(1 - a^2/x^2)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.