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