Sr Examen
Integral de (x^2-3)^(-3/2) dx
Solución
Ha introducido
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6 / | | 1 | ----------- dx | 3/2 | / 2 \ | \x - 3/ | / 2
$$\int\limits_{2}^{6} \frac{1}{\left(x^{2} - 3\right)^{\frac{3}{2}}}\, dx$$
Integral((x^2 - 3)^(-3/2), (x, 2, 6))
Respuesta (Indefinida)
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// | 2| \
|| -x |x | |
||-------------- for ---- > 1|
/ || _________ 3 |
| || / 2 |
| 1 ||3*\/ -3 + x |
| ----------- dx = C + |< |
| 3/2 || I*x |
| / 2 \ ||------------- otherwise |
| \x - 3/ || ________ |
| || / 2 |
/ ||3*\/ 3 - x |
\\ /
$$\int \frac{1}{\left(x^{2} - 3\right)^{\frac{3}{2}}}\, dx = C + \begin{cases} - \frac{x}{3 \sqrt{x^{2} - 3}} & \text{for}\: \frac{\left|{x^{2}}\right|}{3} > 1 \\\frac{i x}{3 \sqrt{3 - x^{2}}} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
6 / | | / 2 2 | | 1 x x | |- -------------- + -------------- for -- > 1 | | _________ 3/2 3 | | / 2 / 2\ | | 3*\/ -3 + x 3*\-3 + x / | < dx | | 2 | | I I*x | | ------------- + ------------- otherwise | | ________ 3/2 | | / 2 / 2\ | \ 3*\/ 3 - x 3*\3 - x / | / 2
$$\int\limits_{2}^{6} \begin{cases} \frac{x^{2}}{3 \left(x^{2} - 3\right)^{\frac{3}{2}}} - \frac{1}{3 \sqrt{x^{2} - 3}} & \text{for}\: \frac{x^{2}}{3} > 1 \\\frac{i x^{2}}{3 \left(3 - x^{2}\right)^{\frac{3}{2}}} + \frac{i}{3 \sqrt{3 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$
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6 / | | / 2 2 | | 1 x x | |- -------------- + -------------- for -- > 1 | | _________ 3/2 3 | | / 2 / 2\ | | 3*\/ -3 + x 3*\-3 + x / | < dx | | 2 | | I I*x | | ------------- + ------------- otherwise | | ________ 3/2 | | / 2 / 2\ | \ 3*\/ 3 - x 3*\3 - x / | / 2
$$\int\limits_{2}^{6} \begin{cases} \frac{x^{2}}{3 \left(x^{2} - 3\right)^{\frac{3}{2}}} - \frac{1}{3 \sqrt{x^{2} - 3}} & \text{for}\: \frac{x^{2}}{3} > 1 \\\frac{i x^{2}}{3 \left(3 - x^{2}\right)^{\frac{3}{2}}} + \frac{i}{3 \sqrt{3 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-1/(3*sqrt(-3 + x^2)) + x^2/(3*(-3 + x^2)^(3/2)), x^2/3 > 1), (i/(3*sqrt(3 - x^2)) + i*x^2/(3*(3 - x^2)^(3/2)), True)), (x, 2, 6))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.