Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acos(x)/x^3+1/(2*x^2*sqrt(1-x^2))-1/(2*x^3*sqrt(1/(x^2)-1))
¿Cómo vas a descomponer esta acos(x)/x^3+1/(2*x^2*sqrt(1-x^2))-1/(2*x^3*sqrt(1/(x^2)-1)) expresión en fracciones?
Solución
Ha introducido
[src]
acos(x) 1 1
------- + ---------------- - ------------------
3 ________ ________
x 2 / 2 3 / 1
2*x *\/ 1 - x 2*x * / -- - 1
/ 2
\/ x
$$\left(\frac{1}{2 x^{2} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{3}}\right) - \frac{1}{2 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}}$$
acos(x)/x^3 + 1/((2*x^2)*sqrt(1 - x^2)) - 1/((2*x^3)*sqrt(1/(x^2) - 1))
Simplificación general
[src]
acos(x) 1 1
------- + ---------------- - -------------------
3 ________ _________
x 2 / 2 3 / 1
2*x *\/ 1 - x 2*x * / -1 + --
/ 2
\/ x
$$\frac{1}{2 x^{2} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{3}} - \frac{1}{2 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}}$$
acos(x)/x^3 + 1/(2*x^2*sqrt(1 - x^2)) - 1/(2*x^3*sqrt(-1 + x^(-2)))
Respuesta numérica
[src]
acos(x)/x^3 + 0.5*(1.0 - x^2)^(-0.5)/x^2 - 0.5*(-1.0 + x^(-2))^(-0.5)/x^3
acos(x)/x^3 + 0.5*(1.0 - x^2)^(-0.5)/x^2 - 0.5*(-1.0 + x^(-2))^(-0.5)/x^3
Denominador común
[src]
________ _________ ________ _________
/ 2 / 1 / 2 / 1
- \/ 1 - x + x* / -1 + -- + 2*\/ 1 - x * / -1 + -- *acos(x)
/ 2 / 2
\/ x \/ x
-----------------------------------------------------------------------
________ _________
3 / 2 / 1
2*x *\/ 1 - x * / -1 + --
/ 2
\/ x
$$\frac{x \sqrt{-1 + \frac{1}{x^{2}}} + 2 \sqrt{-1 + \frac{1}{x^{2}}} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}}{2 x^{3} \sqrt{-1 + \frac{1}{x^{2}}} \sqrt{1 - x^{2}}}$$
(-sqrt(1 - x^2) + x*sqrt(-1 + x^(-2)) + 2*sqrt(1 - x^2)*sqrt(-1 + x^(-2))*acos(x))/(2*x^3*sqrt(1 - x^2)*sqrt(-1 + x^(-2)))
Parte trigonométrica
[src]
acos(x) 1 1
------- + ---------------- - -------------------
3 ________ _________
x 2 / 2 3 / 1
2*x *\/ 1 - x 2*x * / -1 + --
/ 2
\/ x
$$\frac{1}{2 x^{2} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{3}} - \frac{1}{2 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}}$$
acos(x)/x^3 + 1/(2*x^2*sqrt(1 - x^2)) - 1/(2*x^3*sqrt(-1 + x^(-2)))
Denominador racional
[src]
_________ ________ ________ _________
5 5 / 1 6 / 2 4 / 2 7 / 1 3 7
- 8*x *acos(x) - 2*x * / -1 + -- - 2*x *\/ 1 - x + 2*x *\/ 1 - x + 2*x * / -1 + -- + 4*x *acos(x) + 4*x *acos(x)
/ 2 / 2
\/ x \/ x
------------------------------------------------------------------------------------------------------------------------------
8 / 1 \ / 2\
4*x *|1 - --|*\-1 + x /
| 2|
\ x /
$$\frac{2 x^{7} \sqrt{-1 + \frac{1}{x^{2}}} + 4 x^{7} \operatorname{acos}{\left(x \right)} - 2 x^{6} \sqrt{1 - x^{2}} - 2 x^{5} \sqrt{-1 + \frac{1}{x^{2}}} - 8 x^{5} \operatorname{acos}{\left(x \right)} + 2 x^{4} \sqrt{1 - x^{2}} + 4 x^{3} \operatorname{acos}{\left(x \right)}}{4 x^{8} \left(1 - \frac{1}{x^{2}}\right) \left(x^{2} - 1\right)}$$
(-8*x^5*acos(x) - 2*x^5*sqrt(-1 + x^(-2)) - 2*x^6*sqrt(1 - x^2) + 2*x^4*sqrt(1 - x^2) + 2*x^7*sqrt(-1 + x^(-2)) + 4*x^3*acos(x) + 4*x^7*acos(x))/(4*x^8*(1 - 1/x^2)*(-1 + x^2))
Compilar la expresión
[src]
acos(x) 1 1
------- + ---------------- - -------------------
3 ________ _________
x 2 / 2 3 / 1
2*x *\/ 1 - x 2*x * / -1 + --
/ 2
\/ x
$$\frac{1}{2 x^{2} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{3}} - \frac{1}{2 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}}$$
acos(x)/x^3 + 1/(2*x^2*sqrt(1 - x^2)) - 1/(2*x^3*sqrt(-1 + x^(-2)))
Combinatoria
[src]
________ _________ ________ _________
/ 2 / 1 / 2 / 1
- \/ 1 - x + x* / -1 + -- + 2*\/ 1 - x * / -1 + -- *acos(x)
/ 2 / 2
\/ x \/ x
-----------------------------------------------------------------------
__________________
3 / / 1\ / 1\ ___________________
2*x * / |1 + -|*|-1 + -| *\/ -(1 + x)*(-1 + x)
\/ \ x/ \ x/
$$\frac{x \sqrt{-1 + \frac{1}{x^{2}}} + 2 \sqrt{-1 + \frac{1}{x^{2}}} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}}{2 x^{3} \sqrt{\left(-1 + \frac{1}{x}\right) \left(1 + \frac{1}{x}\right)} \sqrt{- \left(x - 1\right) \left(x + 1\right)}}$$
(-sqrt(1 - x^2) + x*sqrt(-1 + x^(-2)) + 2*sqrt(1 - x^2)*sqrt(-1 + x^(-2))*acos(x))/(2*x^3*sqrt((1 + 1/x)*(-1 + 1/x))*sqrt(-(1 + x)*(-1 + x)))
Potencias
[src]
acos(x) 1 1
------- + ---------------- - -------------------
3 ________ _________
x 2 / 2 3 / 1
2*x *\/ 1 - x 2*x * / -1 + --
/ 2
\/ x
$$\frac{1}{2 x^{2} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{3}} - \frac{1}{2 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}}$$
acos(x)/x^3 + 1/(2*x^2*sqrt(1 - x^2)) - 1/(2*x^3*sqrt(-1 + x^(-2)))
Unión de expresiones racionales
[src]
________
________ / 2 / ________ \
/ 2 / 1 - x | / 2 |
- \/ 1 - x + / ------ *\x + 2*\/ 1 - x *acos(x)/
/ 2
\/ x
----------------------------------------------------------
________
/ 2 ________
3 / 1 - x / 2
2*x * / ------ *\/ 1 - x
/ 2
\/ x
$$\frac{\sqrt{\frac{1 - x^{2}}{x^{2}}} \left(x + 2 \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}\right) - \sqrt{1 - x^{2}}}{2 x^{3} \sqrt{\frac{1 - x^{2}}{x^{2}}} \sqrt{1 - x^{2}}}$$
(-sqrt(1 - x^2) + sqrt((1 - x^2)/x^2)*(x + 2*sqrt(1 - x^2)*acos(x)))/(2*x^3*sqrt((1 - x^2)/x^2)*sqrt(1 - x^2))