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