Sr Examen
Integral de dx/sqrt(x^2-1)^3 dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 3 | ________ | / 2 | \/ x - 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(\sqrt{x^{2} - 1}\right)^{3}}\, dx$$
Integral(1/((sqrt(x^2 - 1))^3), (x, 0, 1))
Respuesta (Indefinida)
[src]
// -x | 2| \
||------------ for |x | > 1|
/ || _________ |
| || / 2 |
| 1 ||\/ -1 + x |
| ------------ dx = C + |< |
| 3 || I*x |
| ________ ||----------- otherwise |
| / 2 || ________ |
| \/ x - 1 || / 2 |
| \\\/ 1 - x /
/
$$\int \frac{1}{\left(\sqrt{x^{2} - 1}\right)^{3}}\, dx = C + \begin{cases} - \frac{x}{\sqrt{x^{2} - 1}} & \text{for}\: \left|{x^{2}}\right| > 1 \\\frac{i x}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
1 / | | / 2 | | 1 x 2 | |- ------------ + ------------ for x > 1 | | _________ 3/2 | | / 2 / 2\ | | \/ -1 + x \-1 + x / | < dx | | 2 | | I I*x | | ----------- + ----------- otherwise | | ________ 3/2 | | / 2 / 2\ | \ \/ 1 - x \1 - x / | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{x^{2}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{1}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} > 1 \\\frac{i x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{i}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / 2 | | 1 x 2 | |- ------------ + ------------ for x > 1 | | _________ 3/2 | | / 2 / 2\ | | \/ -1 + x \-1 + x / | < dx | | 2 | | I I*x | | ----------- + ----------- otherwise | | ________ 3/2 | | / 2 / 2\ | \ \/ 1 - x \1 - x / | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{x^{2}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{1}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} > 1 \\\frac{i x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{i}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-1/sqrt(-1 + x^2) + x^2/(-1 + x^2)^(3/2), x^2 > 1), (i/sqrt(1 - x^2) + i*x^2/(1 - x^2)^(3/2), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.