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