Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(x)^(1/4)/x+20*(1-cos(x)^2)^9*cos(x)*sin(x)+log(x)/(4*sqrt(1-x^2)*asin(x)^(3/4))
¿Cómo vas a descomponer esta asin(x)^(1/4)/x+20*(1-cos(x)^2)^9*cos(x)*sin(x)+log(x)/(4*sqrt(1-x^2)*asin(x)^(3/4)) expresión en fracciones?
Solución
Ha introducido
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4 _________ 9
\/ asin(x) / 2 \ log(x)
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
x ________
/ 2 3/4
4*\/ 1 - x *asin (x)
$$\left(20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \cos{\left(x \right)} \sin{\left(x \right)} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x}\right) + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}$$
asin(x)^(1/4)/x + ((20*(1 - cos(x)^2)^9)*cos(x))*sin(x) + log(x)/(((4*sqrt(1 - x^2))*asin(x)^(3/4)))
Simplificación general
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4 _________
\/ asin(x) 19 log(x)
----------- + 20*sin (x)*cos(x) + ------------------------
x ________
/ 2 3/4
4*\/ 1 - x *asin (x)
$$20 \sin^{19}{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x}$$
asin(x)^(1/4)/x + 20*sin(x)^19*cos(x) + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4))
Respuesta numérica
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asin(x)^0.25/x + 0.25*(1.0 - x^2)^(-0.5)*asin(x)^(-0.75)*log(x) + 20.0*(1.0 - cos(x)^2)^9*cos(x)*sin(x)
asin(x)^0.25/x + 0.25*(1.0 - x^2)^(-0.5)*asin(x)^(-0.75)*log(x) + 20.0*(1.0 - cos(x)^2)^9*cos(x)*sin(x)
Unión de expresiones racionales
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________ / 9 \
/ 2 3/4 |4 _________ / 2 \ |
x*log(x) + 4*\/ 1 - x *asin (x)*\\/ asin(x) + 20*x*\1 - cos (x)/ *cos(x)*sin(x)/
-------------------------------------------------------------------------------------
________
/ 2 3/4
4*x*\/ 1 - x *asin (x)
$$\frac{x \log{\left(x \right)} + 4 \sqrt{1 - x^{2}} \left(20 x \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} + \sqrt[4]{\operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}{4 x \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}$$
(x*log(x) + 4*sqrt(1 - x^2)*asin(x)^(3/4)*(asin(x)^(1/4) + 20*x*(1 - cos(x)^2)^9*cos(x)*sin(x)))/(4*x*sqrt(1 - x^2)*asin(x)^(3/4))
Denominador común
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________
/ 2
11 7 15 3 19 17 5 13 9 x*log(x) + 4*\/ 1 - x *asin(x)
- 2520*cos (x)*sin(x) - 1680*cos (x)*sin(x) - 720*cos (x)*sin(x) - 180*cos (x)*sin(x) - 20*cos (x)*sin(x) + 20*cos(x)*sin(x) + 180*cos (x)*sin(x) + 720*cos (x)*sin(x) + 1680*cos (x)*sin(x) + 2520*cos (x)*sin(x) + --------------------------------
________
/ 2 3/4
4*x*\/ 1 - x *asin (x)
$$- 20 \sin{\left(x \right)} \cos^{19}{\left(x \right)} + 180 \sin{\left(x \right)} \cos^{17}{\left(x \right)} - 720 \sin{\left(x \right)} \cos^{15}{\left(x \right)} + 1680 \sin{\left(x \right)} \cos^{13}{\left(x \right)} - 2520 \sin{\left(x \right)} \cos^{11}{\left(x \right)} + 2520 \sin{\left(x \right)} \cos^{9}{\left(x \right)} - 1680 \sin{\left(x \right)} \cos^{7}{\left(x \right)} + 720 \sin{\left(x \right)} \cos^{5}{\left(x \right)} - 180 \sin{\left(x \right)} \cos^{3}{\left(x \right)} + 20 \sin{\left(x \right)} \cos{\left(x \right)} + \frac{x \log{\left(x \right)} + 4 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4 x \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}$$
-2520*cos(x)^11*sin(x) - 1680*cos(x)^7*sin(x) - 720*cos(x)^15*sin(x) - 180*cos(x)^3*sin(x) - 20*cos(x)^19*sin(x) + 20*cos(x)*sin(x) + 180*cos(x)^17*sin(x) + 720*cos(x)^5*sin(x) + 1680*cos(x)^13*sin(x) + 2520*cos(x)^9*sin(x) + (x*log(x) + 4*sqrt(1 - x^2)*asin(x))/(4*x*sqrt(1 - x^2)*asin(x)^(3/4))
Denominador racional
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________ 9 9
2 / 2 3 / 2 \ 3/4 / 2 \ 3/4
-4*asin(x) + 4*x *asin(x) - x*\/ 1 - x *log(x) - 80*x *\-1 + cos (x)/ *asin (x)*cos(x)*sin(x) + 80*x*\-1 + cos (x)/ *asin (x)*cos(x)*sin(x)
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/ 2\ 3/4
4*x*\-1 + x /*asin (x)
$$\frac{- 80 x^{3} \left(\cos^{2}{\left(x \right)} - 1\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 4 x^{2} \operatorname{asin}{\left(x \right)} - x \sqrt{1 - x^{2}} \log{\left(x \right)} + 80 x \left(\cos^{2}{\left(x \right)} - 1\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 4 \operatorname{asin}{\left(x \right)}}{4 x \left(x^{2} - 1\right) \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}$$
(-4*asin(x) + 4*x^2*asin(x) - x*sqrt(1 - x^2)*log(x) - 80*x^3*(-1 + cos(x)^2)^9*asin(x)^(3/4)*cos(x)*sin(x) + 80*x*(-1 + cos(x)^2)^9*asin(x)^(3/4)*cos(x)*sin(x))/(4*x*(-1 + x^2)*asin(x)^(3/4))
Potencias
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4 _________ 9
\/ asin(x) / 2 \ log(x)
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
x ________
/ 2 3/4
4*\/ 1 - x *asin (x)
$$20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x}$$
9
/ 2\
4 _________ | / I*x -I*x\ | / I*x -I*x\
\/ asin(x) log(x) | |e e | | |e e | / -I*x I*x\
----------- + ------------------------ - 10*I*|1 - |---- + -----| | *|---- + -----|*\- e + e /
x ________ \ \ 2 2 / / \ 2 2 /
/ 2 3/4
4*\/ 1 - x *asin (x)
$$- 10 i \left(1 - \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}\right)^{9} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{i x} - e^{- i x}\right) + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x}$$
asin(x)^(1/4)/x + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4)) - 10*i*(1 - (exp(i*x)/2 + exp(-i*x)/2)^2)^9*(exp(i*x)/2 + exp(-i*x)/2)*(-exp(-i*x) + exp(i*x))
Combinatoria
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/ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ \
| / 2 / 2 3/4 9 / 2 3/4 13 / 2 3/4 5 / 2 3/4 17 / 2 3/4 / 2 3/4 19 / 2 3/4 3 / 2 3/4 15 / 2 3/4 7 / 2 3/4 11 |
-\-x*log(x) - 4*\/ 1 - x *asin(x) - 10080*x*\/ 1 - x *asin (x)*cos (x)*sin(x) - 6720*x*\/ 1 - x *asin (x)*cos (x)*sin(x) - 2880*x*\/ 1 - x *asin (x)*cos (x)*sin(x) - 720*x*\/ 1 - x *asin (x)*cos (x)*sin(x) - 80*x*\/ 1 - x *asin (x)*cos(x)*sin(x) + 80*x*\/ 1 - x *asin (x)*cos (x)*sin(x) + 720*x*\/ 1 - x *asin (x)*cos (x)*sin(x) + 2880*x*\/ 1 - x *asin (x)*cos (x)*sin(x) + 6720*x*\/ 1 - x *asin (x)*cos (x)*sin(x) + 10080*x*\/ 1 - x *asin (x)*cos (x)*sin(x)/
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___________________ 3/4
4*x*\/ -(1 + x)*(-1 + x) *asin (x)
$$- \frac{80 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{19}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{17}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 2880 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{15}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 6720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{13}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 10080 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{11}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 10080 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{9}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 6720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{7}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 2880 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{5}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{3}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 80 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - x \log{\left(x \right)} - 4 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4 x \sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}$$
-(-x*log(x) - 4*sqrt(1 - x^2)*asin(x) - 10080*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^9*sin(x) - 6720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^13*sin(x) - 2880*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^5*sin(x) - 720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^17*sin(x) - 80*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)*sin(x) + 80*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^19*sin(x) + 720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^3*sin(x) + 2880*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^15*sin(x) + 6720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^7*sin(x) + 10080*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^11*sin(x))/(4*x*sqrt(-(1 + x)*(-1 + x))*asin(x)^(3/4))
Compilar la expresión
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4 _________ 9
\/ asin(x) / 2 \ log(x)
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
x ________
/ 2 3/4
4*\/ 1 - x *asin (x)
$$20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x}$$
asin(x)^(1/4)/x + 20*(1 - cos(x)^2)^9*cos(x)*sin(x) + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4))