Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acos(x)^4*(1+2*x)/(x^2+x-1)-4*acos(x)^3*log(x^2+x-1)/sqrt(1-x^2)
¿Cómo vas a descomponer esta acos(x)^4*(1+2*x)/(x^2+x-1)-4*acos(x)^3*log(x^2+x-1)/sqrt(1-x^2) expresión en fracciones?
Solución
Ha introducido
[src]
4 3 / 2 \
acos (x)*(1 + 2*x) 4*acos (x)*log\x + x - 1/
------------------ - --------------------------
2 ________
x + x - 1 / 2
\/ 1 - x
$$\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{\left(x^{2} + x\right) - 1} - \frac{\log{\left(\left(x^{2} + x\right) - 1 \right)} 4 \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
(acos(x)^4*(1 + 2*x))/(x^2 + x - 1) - (4*acos(x)^3)*log(x^2 + x - 1)/sqrt(1 - x^2)
Simplificación general
[src]
/ ________ \
3 | / 2\ / 2\ / 2 |
acos (x)*\- 4*\-1 + x + x /*log\-1 + x + x / + \/ 1 - x *(1 + 2*x)*acos(x)/
-----------------------------------------------------------------------------
________
/ 2 / 2\
\/ 1 - x *\-1 + x + x /
$$\frac{\left(\sqrt{1 - x^{2}} \left(2 x + 1\right) \operatorname{acos}{\left(x \right)} - 4 \left(x^{2} + x - 1\right) \log{\left(x^{2} + x - 1 \right)}\right) \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x^{2} + x - 1\right)}$$
acos(x)^3*(-4*(-1 + x + x^2)*log(-1 + x + x^2) + sqrt(1 - x^2)*(1 + 2*x)*acos(x))/(sqrt(1 - x^2)*(-1 + x + x^2))
Parte trigonométrica
[src]
4 3 / 2\
acos (x)*(1 + 2*x) 4*acos (x)*log\-1 + x + x /
------------------ - ---------------------------
2 ________
-1 + x + x / 2
\/ 1 - x
$$\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{x^{2} + x - 1} - \frac{4 \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
acos(x)^4*(1 + 2*x)/(-1 + x + x^2) - 4*acos(x)^3*log(-1 + x + x^2)/sqrt(1 - x^2)
Potencias
[src]
4 3 / 2\
acos (x)*(1 + 2*x) 4*acos (x)*log\-1 + x + x /
------------------ - ---------------------------
2 ________
-1 + x + x / 2
\/ 1 - x
$$\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{x^{2} + x - 1} - \frac{4 \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
acos(x)^4*(1 + 2*x)/(-1 + x + x^2) - 4*acos(x)^3*log(-1 + x + x^2)/sqrt(1 - x^2)
Unión de expresiones racionales
[src]
/ ________ \
3 | / 2 |
acos (x)*\-4*(-1 + x*(1 + x))*log(-1 + x*(1 + x)) + \/ 1 - x *(1 + 2*x)*acos(x)/
----------------------------------------------------------------------------------
________
/ 2
\/ 1 - x *(-1 + x*(1 + x))
$$\frac{\left(\sqrt{1 - x^{2}} \left(2 x + 1\right) \operatorname{acos}{\left(x \right)} - 4 \left(x \left(x + 1\right) - 1\right) \log{\left(x \left(x + 1\right) - 1 \right)}\right) \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x \left(x + 1\right) - 1\right)}$$
acos(x)^3*(-4*(-1 + x*(1 + x))*log(-1 + x*(1 + x)) + sqrt(1 - x^2)*(1 + 2*x)*acos(x))/(sqrt(1 - x^2)*(-1 + x*(1 + x)))
Combinatoria
[src]
/ ________ ________ \
3 | / 2\ / 2 / 2\ 2 / 2\ / 2 |
-acos (x)*\- 4*log\-1 + x + x / - \/ 1 - x *acos(x) + 4*x*log\-1 + x + x / + 4*x *log\-1 + x + x / - 2*x*\/ 1 - x *acos(x)/
--------------------------------------------------------------------------------------------------------------------------------
___________________ / 2\
\/ -(1 + x)*(-1 + x) *\-1 + x + x /
$$- \frac{\left(4 x^{2} \log{\left(x^{2} + x - 1 \right)} - 2 x \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + 4 x \log{\left(x^{2} + x - 1 \right)} - \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - 4 \log{\left(x^{2} + x - 1 \right)}\right) \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + x - 1\right)}$$
-acos(x)^3*(-4*log(-1 + x + x^2) - sqrt(1 - x^2)*acos(x) + 4*x*log(-1 + x + x^2) + 4*x^2*log(-1 + x + x^2) - 2*x*sqrt(1 - x^2)*acos(x))/(sqrt(-(1 + x)*(-1 + x))*(-1 + x + x^2))
Denominador común
[src]
/ ________ ________ \
| / 2 4 3 / 2\ / 2 4 3 / 2\ 2 3 / 2\|
-\- \/ 1 - x *acos (x) - 4*acos (x)*log\-1 + x + x / - 2*x*\/ 1 - x *acos (x) + 4*x*acos (x)*log\-1 + x + x / + 4*x *acos (x)*log\-1 + x + x //
----------------------------------------------------------------------------------------------------------------------------------------------------
________ ________ ________
/ 2 / 2 2 / 2
- \/ 1 - x + x*\/ 1 - x + x *\/ 1 - x
$$- \frac{4 x^{2} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - 2 x \sqrt{1 - x^{2}} \operatorname{acos}^{4}{\left(x \right)} + 4 x \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - \sqrt{1 - x^{2}} \operatorname{acos}^{4}{\left(x \right)} - 4 \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} + x \sqrt{1 - x^{2}} - \sqrt{1 - x^{2}}}$$
-(-sqrt(1 - x^2)*acos(x)^4 - 4*acos(x)^3*log(-1 + x + x^2) - 2*x*sqrt(1 - x^2)*acos(x)^4 + 4*x*acos(x)^3*log(-1 + x + x^2) + 4*x^2*acos(x)^3*log(-1 + x + x^2))/(-sqrt(1 - x^2) + x*sqrt(1 - x^2) + x^2*sqrt(1 - x^2))
Compilar la expresión
[src]
4 3 / 2 \
acos (x)*(1 + 2*x) 4*acos (x)*log\x + x - 1/
------------------ - --------------------------
2 ________
-1 + x + x / 2
\/ 1 - x
$$\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{x^{2} + x - 1} - \frac{4 \log{\left(\left(x^{2} + x\right) - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
acos(x)^4*(1 + 2*x)/(-1 + x + x^2) - 4*acos(x)^3*log(x^2 + x - 1)/sqrt(1 - x^2)
Denominador racional
[src]
________ ________ ________
4 2 4 4 3 4 / 2 3 / 2\ / 2 3 / 2\ 2 / 2 3 / 2\
- acos (x) + x *acos (x) - 2*x*acos (x) + 2*x *acos (x) - 4*\/ 1 - x *acos (x)*log\-1 + x + x / + 4*x*\/ 1 - x *acos (x)*log\-1 + x + x / + 4*x *\/ 1 - x *acos (x)*log\-1 + x + x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ / 2\
\-1 + x /*\-1 + x + x /
$$\frac{2 x^{3} \operatorname{acos}^{4}{\left(x \right)} + 4 x^{2} \sqrt{1 - x^{2}} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} + x^{2} \operatorname{acos}^{4}{\left(x \right)} + 4 x \sqrt{1 - x^{2}} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - 2 x \operatorname{acos}^{4}{\left(x \right)} - 4 \sqrt{1 - x^{2}} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - \operatorname{acos}^{4}{\left(x \right)}}{\left(x^{2} - 1\right) \left(x^{2} + x - 1\right)}$$
(-acos(x)^4 + x^2*acos(x)^4 - 2*x*acos(x)^4 + 2*x^3*acos(x)^4 - 4*sqrt(1 - x^2)*acos(x)^3*log(-1 + x + x^2) + 4*x*sqrt(1 - x^2)*acos(x)^3*log(-1 + x + x^2) + 4*x^2*sqrt(1 - x^2)*acos(x)^3*log(-1 + x + x^2))/((-1 + x^2)*(-1 + x + x^2))
Respuesta numérica
[src]
acos(x)^4*(1.0 + 2.0*x)/(-1.0 + x + x^2) - 4.0*(1.0 - x^2)^(-0.5)*acos(x)^3*log(x^2 + x - 1)
acos(x)^4*(1.0 + 2.0*x)/(-1.0 + x + x^2) - 4.0*(1.0 - x^2)^(-0.5)*acos(x)^3*log(x^2 + x - 1)