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