Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acot(3*x)^4/(x-4)-12*acot(3*x)^3*log(x-4)/(1+9*x^2)
¿Cómo vas a descomponer esta acot(3*x)^4/(x-4)-12*acot(3*x)^3*log(x-4)/(1+9*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
4 3
acot (3*x) 12*acot (3*x)*log(x - 4)
---------- - ------------------------
x - 4 2
1 + 9*x
$$- \frac{\log{\left(x - 4 \right)} 12 \operatorname{acot}^{3}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\operatorname{acot}^{4}{\left(3 x \right)}}{x - 4}$$
acot(3*x)^4/(x - 4) - (12*acot(3*x)^3)*log(x - 4)/(1 + 9*x^2)
Simplificación general
[src]
3 // 2\ \
acot (3*x)*\\1 + 9*x /*acot(3*x) - 12*(-4 + x)*log(-4 + x)/
-----------------------------------------------------------
/ 2\
\1 + 9*x /*(-4 + x)
$$\frac{\left(- 12 \left(x - 4\right) \log{\left(x - 4 \right)} + \left(9 x^{2} + 1\right) \operatorname{acot}{\left(3 x \right)}\right) \operatorname{acot}^{3}{\left(3 x \right)}}{\left(x - 4\right) \left(9 x^{2} + 1\right)}$$
acot(3*x)^3*((1 + 9*x^2)*acot(3*x) - 12*(-4 + x)*log(-4 + x))/((1 + 9*x^2)*(-4 + x))
Respuesta numérica
[src]
acot(3*x)^4/(-4.0 + x) - 12.0*acot(3*x)^3*log(x - 4)/(1.0 + 9.0*x^2)
acot(3*x)^4/(-4.0 + x) - 12.0*acot(3*x)^3*log(x - 4)/(1.0 + 9.0*x^2)
Combinatoria
[src]
3 / 2 \
acot (3*x)*\48*log(-4 + x) - 12*x*log(-4 + x) + 9*x *acot(3*x) + acot(3*x)/
---------------------------------------------------------------------------
/ 2\
\1 + 9*x /*(-4 + x)
$$\frac{\left(9 x^{2} \operatorname{acot}{\left(3 x \right)} - 12 x \log{\left(x - 4 \right)} + 48 \log{\left(x - 4 \right)} + \operatorname{acot}{\left(3 x \right)}\right) \operatorname{acot}^{3}{\left(3 x \right)}}{\left(x - 4\right) \left(9 x^{2} + 1\right)}$$
acot(3*x)^3*(48*log(-4 + x) - 12*x*log(-4 + x) + 9*x^2*acot(3*x) + acot(3*x))/((1 + 9*x^2)*(-4 + x))
Parte trigonométrica
[src]
4 3
acot (3*x) 12*acot (3*x)*log(-4 + x)
---------- - -------------------------
-4 + x 2
1 + 9*x
$$- \frac{12 \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\operatorname{acot}^{4}{\left(3 x \right)}}{x - 4}$$
acot(3*x)^4/(-4 + x) - 12*acot(3*x)^3*log(-4 + x)/(1 + 9*x^2)
Denominador común
[src]
4 2 4 3 3
acot (3*x) + 9*x *acot (3*x) + 48*acot (3*x)*log(-4 + x) - 12*x*acot (3*x)*log(-4 + x)
--------------------------------------------------------------------------------------
2 3
-4 + x - 36*x + 9*x
$$\frac{9 x^{2} \operatorname{acot}^{4}{\left(3 x \right)} - 12 x \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)} + 48 \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)} + \operatorname{acot}^{4}{\left(3 x \right)}}{9 x^{3} - 36 x^{2} + x - 4}$$
(acot(3*x)^4 + 9*x^2*acot(3*x)^4 + 48*acot(3*x)^3*log(-4 + x) - 12*x*acot(3*x)^3*log(-4 + x))/(-4 + x - 36*x^2 + 9*x^3)
Unión de expresiones racionales
[src]
3 // 2\ \
acot (3*x)*\\1 + 9*x /*acot(3*x) - 12*(-4 + x)*log(-4 + x)/
-----------------------------------------------------------
/ 2\
\1 + 9*x /*(-4 + x)
$$\frac{\left(- 12 \left(x - 4\right) \log{\left(x - 4 \right)} + \left(9 x^{2} + 1\right) \operatorname{acot}{\left(3 x \right)}\right) \operatorname{acot}^{3}{\left(3 x \right)}}{\left(x - 4\right) \left(9 x^{2} + 1\right)}$$
acot(3*x)^3*((1 + 9*x^2)*acot(3*x) - 12*(-4 + x)*log(-4 + x))/((1 + 9*x^2)*(-4 + x))
Denominador racional
[src]
4 2 4 3 3
acot (3*x) + 9*x *acot (3*x) + 48*acot (3*x)*log(-4 + x) - 12*x*acot (3*x)*log(-4 + x)
--------------------------------------------------------------------------------------
/ 2\
\1 + 9*x /*(-4 + x)
$$\frac{9 x^{2} \operatorname{acot}^{4}{\left(3 x \right)} - 12 x \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)} + 48 \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)} + \operatorname{acot}^{4}{\left(3 x \right)}}{\left(x - 4\right) \left(9 x^{2} + 1\right)}$$
(acot(3*x)^4 + 9*x^2*acot(3*x)^4 + 48*acot(3*x)^3*log(-4 + x) - 12*x*acot(3*x)^3*log(-4 + x))/((1 + 9*x^2)*(-4 + x))
Potencias
[src]
4 3
acot (3*x) 12*acot (3*x)*log(-4 + x)
---------- - -------------------------
-4 + x 2
1 + 9*x
$$- \frac{12 \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\operatorname{acot}^{4}{\left(3 x \right)}}{x - 4}$$
acot(3*x)^4/(-4 + x) - 12*acot(3*x)^3*log(-4 + x)/(1 + 9*x^2)
Compilar la expresión
[src]
4 3
acot (3*x) 12*acot (3*x)*log(x - 4)
---------- - ------------------------
-4 + x 2
1 + 9*x
$$- \frac{12 \log{\left(x - 4 \right)} \operatorname{acot}^{3}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\operatorname{acot}^{4}{\left(3 x \right)}}{x - 4}$$
acot(3*x)^4/(-4 + x) - 12*acot(3*x)^3*log(x - 4)/(1 + 9*x^2)