Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acos(3*x)/((x+5)*log(3))-3*log(x+5)/(sqrt(1-9*x^2)*log(3))
¿Cómo vas a descomponer esta acos(3*x)/((x+5)*log(3))-3*log(x+5)/(sqrt(1-9*x^2)*log(3)) expresión en fracciones?
Solución
Ha introducido
[src]
acos(3*x) 3*log(x + 5)
-------------- - --------------------
(x + 5)*log(3) __________
/ 2
\/ 1 - 9*x *log(3)
$$\frac{\operatorname{acos}{\left(3 x \right)}}{\left(x + 5\right) \log{\left(3 \right)}} - \frac{3 \log{\left(x + 5 \right)}}{\sqrt{1 - 9 x^{2}} \log{\left(3 \right)}}$$
acos(3*x)/(((x + 5)*log(3))) - 3*log(x + 5)/(sqrt(1 - 9*x^2)*log(3))
Simplificación general
[src]
__________
/ 2
\/ 1 - 9*x *acos(3*x) - 3*(5 + x)*log(5 + x)
----------------------------------------------
__________
/ 2
\/ 1 - 9*x *(5 + x)*log(3)
$$\frac{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 3 \left(x + 5\right) \log{\left(x + 5 \right)}}{\sqrt{1 - 9 x^{2}} \left(x + 5\right) \log{\left(3 \right)}}$$
(sqrt(1 - 9*x^2)*acos(3*x) - 3*(5 + x)*log(5 + x))/(sqrt(1 - 9*x^2)*(5 + x)*log(3))
Denominador racional
[src]
__________ __________
2 / 2 / 2
-acos(3*x)*log(3) + 9*x *acos(3*x)*log(3) + 15*\/ 1 - 9*x *log(3)*log(5 + x) + 3*x*\/ 1 - 9*x *log(3)*log(5 + x)
--------------------------------------------------------------------------------------------------------------------
/ 2\ 2
\-1 + 9*x /*(5 + x)*log (3)
$$\frac{9 x^{2} \log{\left(3 \right)} \operatorname{acos}{\left(3 x \right)} + 3 x \sqrt{1 - 9 x^{2}} \log{\left(3 \right)} \log{\left(x + 5 \right)} + 15 \sqrt{1 - 9 x^{2}} \log{\left(3 \right)} \log{\left(x + 5 \right)} - \log{\left(3 \right)} \operatorname{acos}{\left(3 x \right)}}{\left(x + 5\right) \left(9 x^{2} - 1\right) \log{\left(3 \right)}^{2}}$$
(-acos(3*x)*log(3) + 9*x^2*acos(3*x)*log(3) + 15*sqrt(1 - 9*x^2)*log(3)*log(5 + x) + 3*x*sqrt(1 - 9*x^2)*log(3)*log(5 + x))/((-1 + 9*x^2)*(5 + x)*log(3)^2)
Unión de expresiones racionales
[src]
__________
/ 2
\/ 1 - 9*x *acos(3*x) - 3*(5 + x)*log(5 + x)
----------------------------------------------
__________
/ 2
\/ 1 - 9*x *(5 + x)*log(3)
$$\frac{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 3 \left(x + 5\right) \log{\left(x + 5 \right)}}{\sqrt{1 - 9 x^{2}} \left(x + 5\right) \log{\left(3 \right)}}$$
(sqrt(1 - 9*x^2)*acos(3*x) - 3*(5 + x)*log(5 + x))/(sqrt(1 - 9*x^2)*(5 + x)*log(3))
Combinatoria
[src]
/ __________ \
| / 2 |
-\15*log(5 + x) - \/ 1 - 9*x *acos(3*x) + 3*x*log(5 + x)/
------------------------------------------------------------
_______________________
\/ -(1 + 3*x)*(-1 + 3*x) *(5 + x)*log(3)
$$- \frac{3 x \log{\left(x + 5 \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} + 15 \log{\left(x + 5 \right)}}{\sqrt{- \left(3 x - 1\right) \left(3 x + 1\right)} \left(x + 5\right) \log{\left(3 \right)}}$$
-(15*log(5 + x) - sqrt(1 - 9*x^2)*acos(3*x) + 3*x*log(5 + x))/(sqrt(-(1 + 3*x)*(-1 + 3*x))*(5 + x)*log(3))
Denominador común
[src]
/ __________ \
| / 2 |
-\15*log(5 + x) - \/ 1 - 9*x *acos(3*x) + 3*x*log(5 + x)/
------------------------------------------------------------
__________ __________
/ 2 / 2
5*\/ 1 - 9*x *log(3) + x*\/ 1 - 9*x *log(3)
$$- \frac{3 x \log{\left(x + 5 \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} + 15 \log{\left(x + 5 \right)}}{x \sqrt{1 - 9 x^{2}} \log{\left(3 \right)} + 5 \sqrt{1 - 9 x^{2}} \log{\left(3 \right)}}$$
-(15*log(5 + x) - sqrt(1 - 9*x^2)*acos(3*x) + 3*x*log(5 + x))/(5*sqrt(1 - 9*x^2)*log(3) + x*sqrt(1 - 9*x^2)*log(3))
Respuesta numérica
[src]
acos(3*x)/(5.49306144334055 + 1.09861228866811*x) - 0.910239226626837*(0.111111111111111 - x^2)^(-0.5)*log(x + 5)
acos(3*x)/(5.49306144334055 + 1.09861228866811*x) - 0.910239226626837*(0.111111111111111 - x^2)^(-0.5)*log(x + 5)