Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acos(3*x)^4/(x-3)-12*acos(3*x)^3*log(x-3)/sqrt(1-9*x^2)
¿Cómo vas a descomponer esta acos(3*x)^4/(x-3)-12*acos(3*x)^3*log(x-3)/sqrt(1-9*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
4 3
acos (3*x) 12*acos (3*x)*log(x - 3)
---------- - ------------------------
x - 3 __________
/ 2
\/ 1 - 9*x
$$- \frac{\log{\left(x - 3 \right)} 12 \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} + \frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3}$$
acos(3*x)^4/(x - 3) - (12*acos(3*x)^3)*log(x - 3)/sqrt(1 - 9*x^2)
Simplificación general
[src]
/ __________ \
3 | / 2 |
acos (3*x)*\\/ 1 - 9*x *acos(3*x) - 12*(-3 + x)*log(-3 + x)/
--------------------------------------------------------------
__________
/ 2
\/ 1 - 9*x *(-3 + x)
$$\frac{\left(\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 12 \left(x - 3\right) \log{\left(x - 3 \right)}\right) \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \left(x - 3\right)}$$
acos(3*x)^3*(sqrt(1 - 9*x^2)*acos(3*x) - 12*(-3 + x)*log(-3 + x))/(sqrt(1 - 9*x^2)*(-3 + x))
Respuesta numérica
[src]
acos(3*x)^4/(-3.0 + x) - 4.0*(0.111111111111111 - x^2)^(-0.5)*acos(3*x)^3*log(x - 3)
acos(3*x)^4/(-3.0 + x) - 4.0*(0.111111111111111 - x^2)^(-0.5)*acos(3*x)^3*log(x - 3)
Parte trigonométrica
[src]
4 3
acos (3*x) 12*acos (3*x)*log(-3 + x)
---------- - -------------------------
-3 + x __________
/ 2
\/ 1 - 9*x
$$\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} - \frac{12 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}$$
acos(3*x)^4/(-3 + x) - 12*acos(3*x)^3*log(-3 + x)/sqrt(1 - 9*x^2)
Combinatoria
[src]
/ __________ \
3 | / 2 |
-acos (3*x)*\-36*log(-3 + x) - \/ 1 - 9*x *acos(3*x) + 12*x*log(-3 + x)/
---------------------------------------------------------------------------
_______________________
\/ -(1 + 3*x)*(-1 + 3*x) *(-3 + x)
$$- \frac{\left(12 x \log{\left(x - 3 \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 36 \log{\left(x - 3 \right)}\right) \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{- \left(3 x - 1\right) \left(3 x + 1\right)} \left(x - 3\right)}$$
-acos(3*x)^3*(-36*log(-3 + x) - sqrt(1 - 9*x^2)*acos(3*x) + 12*x*log(-3 + x))/(sqrt(-(1 + 3*x)*(-1 + 3*x))*(-3 + x))
Potencias
[src]
4 3
acos (3*x) 12*acos (3*x)*log(-3 + x)
---------- - -------------------------
-3 + x __________
/ 2
\/ 1 - 9*x
$$\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} - \frac{12 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}$$
acos(3*x)^4/(-3 + x) - 12*acos(3*x)^3*log(-3 + x)/sqrt(1 - 9*x^2)
Denominador racional
[src]
__________ __________
4 2 4 / 2 3 / 2 3
- acos (3*x) + 9*x *acos (3*x) - 36*\/ 1 - 9*x *acos (3*x)*log(-3 + x) + 12*x*\/ 1 - 9*x *acos (3*x)*log(-3 + x)
--------------------------------------------------------------------------------------------------------------------
/ 2\
\-1 + 9*x /*(-3 + x)
$$\frac{9 x^{2} \operatorname{acos}^{4}{\left(3 x \right)} + 12 x \sqrt{1 - 9 x^{2}} \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)} - 36 \sqrt{1 - 9 x^{2}} \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)} - \operatorname{acos}^{4}{\left(3 x \right)}}{\left(x - 3\right) \left(9 x^{2} - 1\right)}$$
(-acos(3*x)^4 + 9*x^2*acos(3*x)^4 - 36*sqrt(1 - 9*x^2)*acos(3*x)^3*log(-3 + x) + 12*x*sqrt(1 - 9*x^2)*acos(3*x)^3*log(-3 + x))/((-1 + 9*x^2)*(-3 + x))
Unión de expresiones racionales
[src]
/ __________ \
3 | / 2 |
acos (3*x)*\\/ 1 - 9*x *acos(3*x) - 12*(-3 + x)*log(-3 + x)/
--------------------------------------------------------------
__________
/ 2
\/ 1 - 9*x *(-3 + x)
$$\frac{\left(\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 12 \left(x - 3\right) \log{\left(x - 3 \right)}\right) \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \left(x - 3\right)}$$
acos(3*x)^3*(sqrt(1 - 9*x^2)*acos(3*x) - 12*(-3 + x)*log(-3 + x))/(sqrt(1 - 9*x^2)*(-3 + x))
Denominador común
[src]
/ __________ \
| / 2 4 3 3 |
-\- \/ 1 - 9*x *acos (3*x) - 36*acos (3*x)*log(-3 + x) + 12*x*acos (3*x)*log(-3 + x)/
----------------------------------------------------------------------------------------
__________ __________
/ 2 / 2
- 3*\/ 1 - 9*x + x*\/ 1 - 9*x
$$- \frac{12 x \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}^{4}{\left(3 x \right)} - 36 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{x \sqrt{1 - 9 x^{2}} - 3 \sqrt{1 - 9 x^{2}}}$$
-(-sqrt(1 - 9*x^2)*acos(3*x)^4 - 36*acos(3*x)^3*log(-3 + x) + 12*x*acos(3*x)^3*log(-3 + x))/(-3*sqrt(1 - 9*x^2) + x*sqrt(1 - 9*x^2))
Compilar la expresión
[src]
4 3
acos (3*x) 12*acos (3*x)*log(x - 3)
---------- - ------------------------
-3 + x __________
/ 2
\/ 1 - 9*x
$$\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} - \frac{12 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}$$
acos(3*x)^4/(-3 + x) - 12*acos(3*x)^3*log(x - 3)/sqrt(1 - 9*x^2)