Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
Piecewise((x+i*acosh(x)/2+i*x/(2*sqrt(-1+x^2))-i*x^3/(2*sqrt(-1+x^2)),|x^2|>1),(x-asin(x)/2-x*sqrt(1-x^2)/2,True))
¿Cómo vas a descomponer esta Piecewise((x+i*acosh(x)/2+i*x/(2*sqrt(-1+x^2))-i*x^3/(2*sqrt(-1+x^2)),|x^2|>1),(x-asin(x)/2-x*sqrt(1-x^2)/2,True)) expresión en fracciones?
Solución
Ha introducido
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/ 3 | I*acosh(x) I*x I*x | 2| |x + ---------- + -------------- - -------------- for |x | > 1 | 2 _________ _________ | / 2 / 2 | 2*\/ -1 + x 2*\/ -1 + x < | ________ | / 2 | asin(x) x*\/ 1 - x | x - ------- - ------------- otherwise | 2 2 \
$$\begin{cases} - \frac{i x^{3}}{2 \sqrt{x^{2} - 1}} + x + \frac{i x}{2 \sqrt{x^{2} - 1}} + \frac{i \operatorname{acosh}{\left(x \right)}}{2} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \frac{x \sqrt{1 - x^{2}}}{2} + x - \frac{\operatorname{asin}{\left(x \right)}}{2} & \text{otherwise} \end{cases}$$
Piecewise((x + i*acosh(x)/2 + i*x/(2*sqrt(-1 + x^2)) - i*x^3/(2*sqrt(-1 + x^2)), |x^2| > 1), (x - asin(x)/2 - x*sqrt(1 - x^2)/2, True))
Simplificación general
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/ _________ | / 2 3 |I*x + \/ -1 + x *(2*x + I*acosh(x)) - I*x | 2| |-------------------------------------------- for |x | > 1 | _________ | / 2 < 2*\/ -1 + x | | ________ | / 2 | asin(x) x*\/ 1 - x | x - ------- - ------------- otherwise \ 2 2
$$\begin{cases} \frac{- i x^{3} + i x + \left(2 x + i \operatorname{acosh}{\left(x \right)}\right) \sqrt{x^{2} - 1}}{2 \sqrt{x^{2} - 1}} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \frac{x \sqrt{1 - x^{2}}}{2} + x - \frac{\operatorname{asin}{\left(x \right)}}{2} & \text{otherwise} \end{cases}$$
Piecewise(((i*x + sqrt(-1 + x^2)*(2*x + i*acosh(x)) - i*x^3)/(2*sqrt(-1 + x^2)), |x^2| > 1), (x - asin(x)/2 - x*sqrt(1 - x^2)/2, True))
Respuesta numérica
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Piecewise((x + 0.5*i*acosh(x) + 0.5*i*x*(-1.0 + x^2)^(-0.5) - 0.5*i*x^3*(-1.0 + x^2)^(-0.5), |x^2| > 1), (x - 0.5*asin(x) - 0.5*x*(1.0 - x^2)^0.5, True))
Piecewise((x + 0.5*i*acosh(x) + 0.5*i*x*(-1.0 + x^2)^(-0.5) - 0.5*i*x^3*(-1.0 + x^2)^(-0.5), |x^2| > 1), (x - 0.5*asin(x) - 0.5*x*(1.0 - x^2)^0.5, True))
Unión de expresiones racionales
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/ _________ _________ | 3 / 2 / 2 |I*x - I*x + 2*x*\/ -1 + x + I*\/ -1 + x *acosh(x) | 2| |------------------------------------------------------- for |x | > 1 | _________ | / 2 < 2*\/ -1 + x | | ________ | / 2 | -asin(x) + 2*x - x*\/ 1 - x | ------------------------------ otherwise \ 2
$$\begin{cases} \frac{- i x^{3} + 2 x \sqrt{x^{2} - 1} + i x + i \sqrt{x^{2} - 1} \operatorname{acosh}{\left(x \right)}}{2 \sqrt{x^{2} - 1}} & \text{for}\: \left|{x^{2}}\right| > 1 \\\frac{- x \sqrt{1 - x^{2}} + 2 x - \operatorname{asin}{\left(x \right)}}{2} & \text{otherwise} \end{cases}$$
Piecewise(((i*x - i*x^3 + 2*x*sqrt(-1 + x^2) + i*sqrt(-1 + x^2)*acosh(x))/(2*sqrt(-1 + x^2)), |x^2| > 1), ((-asin(x) + 2*x - x*sqrt(1 - x^2))/2, True))