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