Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acos(x)^(2*x)*(2*log(acos(x))-2*x/(sqrt(1-x^2)*acos(x)))
¿Cómo vas a descomponer esta acos(x)^(2*x)*(2*log(acos(x))-2*x/(sqrt(1-x^2)*acos(x))) expresión en fracciones?
Solución
Ha introducido
[src]
2*x / 2*x \
acos (x)*|2*log(acos(x)) - -------------------|
| ________ |
| / 2 |
\ \/ 1 - x *acos(x)/
$$\left(- \frac{2 x}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + 2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}\right) \operatorname{acos}^{2 x}{\left(x \right)}$$
acos(x)^(2*x)*(2*log(acos(x)) - 2*x/(sqrt(1 - x^2)*acos(x)))
Simplificación general
[src]
2*x
2*x 2*x*acos (x)
2*acos (x)*log(acos(x)) - -------------------
________
/ 2
\/ 1 - x *acos(x)
$$- \frac{2 x \operatorname{acos}^{2 x}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + 2 \log{\left(\operatorname{acos}{\left(x \right)} \right)} \operatorname{acos}^{2 x}{\left(x \right)}$$
2*acos(x)^(2*x)*log(acos(x)) - 2*x*acos(x)^(2*x)/(sqrt(1 - x^2)*acos(x))
Denominador racional
[src]
/ ________ \
-1 + 2*x | / 2 2 |
2*acos (x)*\x*\/ 1 - x - acos(x)*log(acos(x)) + x *acos(x)*log(acos(x))/
----------------------------------------------------------------------------------
2
-1 + x
$$\frac{2 \left(x^{2} \log{\left(\operatorname{acos}{\left(x \right)} \right)} \operatorname{acos}{\left(x \right)} + x \sqrt{1 - x^{2}} - \log{\left(\operatorname{acos}{\left(x \right)} \right)} \operatorname{acos}{\left(x \right)}\right) \operatorname{acos}^{2 x - 1}{\left(x \right)}}{x^{2} - 1}$$
2*acos(x)^(-1 + 2*x)*(x*sqrt(1 - x^2) - acos(x)*log(acos(x)) + x^2*acos(x)*log(acos(x)))/(-1 + x^2)
Potencias
[src]
x
2 / 2*x \
acos (x) *|2*log(acos(x)) - -------------------|
| ________ |
| / 2 |
\ \/ 1 - x *acos(x)/
$$\left(- \frac{2 x}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + 2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}\right) \left(\operatorname{acos}^{2}{\left(x \right)}\right)^{x}$$
(acos(x)^2)^x*(2*log(acos(x)) - 2*x/(sqrt(1 - x^2)*acos(x)))
Combinatoria
[src]
/ ________ \
2*x | / 2 |
-2*acos (x)*\x - \/ 1 - x *acos(x)*log(acos(x))/
----------------------------------------------------
___________________
\/ -(1 + x)*(-1 + x) *acos(x)
$$- \frac{2 \left(x - \sqrt{1 - x^{2}} \log{\left(\operatorname{acos}{\left(x \right)} \right)} \operatorname{acos}{\left(x \right)}\right) \operatorname{acos}^{2 x}{\left(x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{acos}{\left(x \right)}}$$
-2*acos(x)^(2*x)*(x - sqrt(1 - x^2)*acos(x)*log(acos(x)))/(sqrt(-(1 + x)*(-1 + x))*acos(x))
Denominador común
[src]
2*x
2*x 2*x*acos (x)
2*acos (x)*log(acos(x)) - -------------------
________
/ 2
\/ 1 - x *acos(x)
$$- \frac{2 x \operatorname{acos}^{2 x}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + 2 \log{\left(\operatorname{acos}{\left(x \right)} \right)} \operatorname{acos}^{2 x}{\left(x \right)}$$
2*acos(x)^(2*x)*log(acos(x)) - 2*x*acos(x)^(2*x)/(sqrt(1 - x^2)*acos(x))
Respuesta numérica
[src]
acos(x)^(2.0*x)*(2.0*log(acos(x)) - 2.0*x*(1.0 - x^2)^(-0.5)/acos(x))
acos(x)^(2.0*x)*(2.0*log(acos(x)) - 2.0*x*(1.0 - x^2)^(-0.5)/acos(x))
Unión de expresiones racionales
[src]
/ ________ \
2*x | / 2 |
2*acos (x)*\-x + \/ 1 - x *acos(x)*log(acos(x))/
----------------------------------------------------
________
/ 2
\/ 1 - x *acos(x)
$$\frac{2 \left(- x + \sqrt{1 - x^{2}} \log{\left(\operatorname{acos}{\left(x \right)} \right)} \operatorname{acos}{\left(x \right)}\right) \operatorname{acos}^{2 x}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}$$
2*acos(x)^(2*x)*(-x + sqrt(1 - x^2)*acos(x)*log(acos(x)))/(sqrt(1 - x^2)*acos(x))