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