Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
Piecewise((-acosh(1/x)+1/(x*sqrt(-1+x^(-2)))-x/sqrt(-1+x^(-2)),1/|x^2|>1),(i*asin(1/x)+i*x/((sqrt(1/(x^2))*sqrt(1-1)))-i/(x*(sqrt(1/(x^2))*sqrt(1-1))),True))
¿Cómo vas a descomponer esta Piecewise((-acosh(1/x)+1/(x*sqrt(-1+x^(-2)))-x/sqrt(-1+x^(-2)),1/|x^2|>1),(i*asin(1/x)+i*x/((sqrt(1/(x^2))*sqrt(1-1)))-i/(x*(sqrt(1/(x^2))*sqrt(1-1))),True)) expresión en fracciones?
Solución
Ha introducido
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/ /1\ 1 x 1 |- acosh|-| + ---------------- - -------------- for ---- > 1 | \x/ _________ _________ | 2| | / 1 / 1 |x | | x* / -1 + -- / -1 + -- < / 2 / 2 | \/ x \/ x | | /1\ | zoo + I*asin|-| + zoo*x otherwise \ \x/
$$\begin{cases} - \frac{x}{\sqrt{-1 + \frac{1}{x^{2}}}} - \operatorname{acosh}{\left(\frac{1}{x} \right)} + \frac{1}{x \sqrt{-1 + \frac{1}{x^{2}}}} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\tilde{\infty} x + i \operatorname{asin}{\left(\frac{1}{x} \right)} + \tilde{\infty} & \text{otherwise} \end{cases}$$
Piecewise((-acosh(1/x) + 1/(x*sqrt(-1 + x^(-2))) - x/sqrt(-1 + x^(-2)), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Simplificación general
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/ _________ | /1\ / 1 1 |- acosh|-| + x* / -1 + -- for ---- > 1 | \x/ / 2 | 2| < \/ x |x | | | /1\ | zoo + I*asin|-| + zoo*x otherwise \ \x/
$$\begin{cases} x \sqrt{-1 + \frac{1}{x^{2}}} - \operatorname{acosh}{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\tilde{\infty} x + i \operatorname{asin}{\left(\frac{1}{x} \right)} + \tilde{\infty} & \text{otherwise} \end{cases}$$
Piecewise((-acosh(1/x) + x*sqrt(-1 + x^(-2)), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Respuesta numérica
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Piecewise((-acosh(1/x) + (-1.0 + x^(-2))^(-0.5)/x - x*(-1.0 + x^(-2))^(-0.5), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Piecewise((-acosh(1/x) + (-1.0 + x^(-2))^(-0.5)/x - x*(-1.0 + x^(-2))^(-0.5), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Unión de expresiones racionales
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/ ________ | / 2 | 2 / 1 - x /1\ |1 - x - x* / ------ *acosh|-| | / 2 \x/ | \/ x 1 |---------------------------------- for ---- > 1 | ________ | 2| < / 2 |x | | / 1 - x | x* / ------ | / 2 | \/ x | | /1\ | zoo + I*asin|-| + zoo*x otherwise \ \x/
$$\begin{cases} \frac{- x^{2} - x \sqrt{\frac{1 - x^{2}}{x^{2}}} \operatorname{acosh}{\left(\frac{1}{x} \right)} + 1}{x \sqrt{\frac{1 - x^{2}}{x^{2}}}} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\tilde{\infty} x + i \operatorname{asin}{\left(\frac{1}{x} \right)} + \tilde{\infty} & \text{otherwise} \end{cases}$$
Piecewise(((1 - x^2 - x*sqrt((1 - x^2)/x^2)*acosh(1/x))/(x*sqrt((1 - x^2)/x^2)), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))