Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(1-3*x)/sqrt(1-x^2)-3*asin(x)/(1-3*x)
¿Cómo vas a descomponer esta log(1-3*x)/sqrt(1-x^2)-3*asin(x)/(1-3*x) expresión en fracciones?
Solución
Ha introducido
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log(1 - 3*x) 3*asin(x) ------------ - --------- ________ 1 - 3*x / 2 \/ 1 - x
$$\frac{\log{\left(1 - 3 x \right)}}{\sqrt{1 - x^{2}}} - \frac{3 \operatorname{asin}{\left(x \right)}}{1 - 3 x}$$
log(1 - 3*x)/sqrt(1 - x^2) - 3*asin(x)/(1 - 3*x)
Simplificación general
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________
/ 2
(-1 + 3*x)*log(1 - 3*x) + 3*\/ 1 - x *asin(x)
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/ 2
\/ 1 - x *(-1 + 3*x)
$$\frac{3 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} + \left(3 x - 1\right) \log{\left(1 - 3 x \right)}}{\sqrt{1 - x^{2}} \left(3 x - 1\right)}$$
((-1 + 3*x)*log(1 - 3*x) + 3*sqrt(1 - x^2)*asin(x))/(sqrt(1 - x^2)*(-1 + 3*x))
Respuesta numérica
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(1.0 - x^2)^(-0.5)*log(1 - 3*x) - 3.0*asin(x)/(1.0 - 3.0*x)
(1.0 - x^2)^(-0.5)*log(1 - 3*x) - 3.0*asin(x)/(1.0 - 3.0*x)
Unión de expresiones racionales
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/ 2
(1 - 3*x)*log(1 - 3*x) - 3*\/ 1 - x *asin(x)
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/ 2
\/ 1 - x *(1 - 3*x)
$$\frac{\left(1 - 3 x\right) \log{\left(1 - 3 x \right)} - 3 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{\left(1 - 3 x\right) \sqrt{1 - x^{2}}}$$
((1 - 3*x)*log(1 - 3*x) - 3*sqrt(1 - x^2)*asin(x))/(sqrt(1 - x^2)*(1 - 3*x))
Denominador racional
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________ ________
/ 2 2 / 2
-3*asin(x) + \/ 1 - x *log(1 - 3*x) + 3*x *asin(x) - 3*x*\/ 1 - x *log(1 - 3*x)
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/ 2\
\-1 + x /*(-1 + 3*x)
$$\frac{3 x^{2} \operatorname{asin}{\left(x \right)} - 3 x \sqrt{1 - x^{2}} \log{\left(1 - 3 x \right)} + \sqrt{1 - x^{2}} \log{\left(1 - 3 x \right)} - 3 \operatorname{asin}{\left(x \right)}}{\left(3 x - 1\right) \left(x^{2} - 1\right)}$$
(-3*asin(x) + sqrt(1 - x^2)*log(1 - 3*x) + 3*x^2*asin(x) - 3*x*sqrt(1 - x^2)*log(1 - 3*x))/((-1 + x^2)*(-1 + 3*x))
Denominador común
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-log(1 - 3*x) + 3*x*log(1 - 3*x) + 3*\/ 1 - x *asin(x)
--------------------------------------------------------
________ ________
/ 2 / 2
- \/ 1 - x + 3*x*\/ 1 - x
$$\frac{3 x \log{\left(1 - 3 x \right)} + 3 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - \log{\left(1 - 3 x \right)}}{3 x \sqrt{1 - x^{2}} - \sqrt{1 - x^{2}}}$$
(-log(1 - 3*x) + 3*x*log(1 - 3*x) + 3*sqrt(1 - x^2)*asin(x))/(-sqrt(1 - x^2) + 3*x*sqrt(1 - x^2))
Combinatoria
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-log(1 - 3*x) + 3*x*log(1 - 3*x) + 3*\/ 1 - x *asin(x)
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___________________
\/ -(1 + x)*(-1 + x) *(-1 + 3*x)
$$\frac{3 x \log{\left(1 - 3 x \right)} + 3 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - \log{\left(1 - 3 x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(3 x - 1\right)}$$
(-log(1 - 3*x) + 3*x*log(1 - 3*x) + 3*sqrt(1 - x^2)*asin(x))/(sqrt(-(1 + x)*(-1 + x))*(-1 + 3*x))