Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acot(5*x)^2/(x+31/10)-10*acot(5*x)*log(x+31/10)/(1+25*x^2)
¿Cómo vas a descomponer esta acot(5*x)^2/(x+31/10)-10*acot(5*x)*log(x+31/10)/(1+25*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 31\
2 10*acot(5*x)*log|x + --|
acot (5*x) \ 10/
---------- - ------------------------
31 2
x + -- 1 + 25*x
10
$$- \frac{\log{\left(x + \frac{31}{10} \right)} 10 \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{x + \frac{31}{10}}$$
acot(5*x)^2/(x + 31/10) - (10*acot(5*x))*log(x + 31/10)/(1 + 25*x^2)
Simplificación general
[src]
// 2\ /31 \\
10*|\1 + 25*x /*acot(5*x) - (31 + 10*x)*log|-- + x||*acot(5*x)
\ \10 //
--------------------------------------------------------------
/ 2\
\1 + 25*x /*(31 + 10*x)
$$\frac{10 \left(- \left(10 x + 31\right) \log{\left(x + \frac{31}{10} \right)} + \left(25 x^{2} + 1\right) \operatorname{acot}{\left(5 x \right)}\right) \operatorname{acot}{\left(5 x \right)}}{\left(10 x + 31\right) \left(25 x^{2} + 1\right)}$$
10*((1 + 25*x^2)*acot(5*x) - (31 + 10*x)*log(31/10 + x))*acot(5*x)/((1 + 25*x^2)*(31 + 10*x))
Denominador común
[src]
2 /31 \ 2 2 /31 \
10*acot (5*x) - 310*acot(5*x)*log|-- + x| + 250*x *acot (5*x) - 100*x*acot(5*x)*log|-- + x|
\10 / \10 /
-------------------------------------------------------------------------------------------
3 2
31 + 10*x + 250*x + 775*x
$$\frac{250 x^{2} \operatorname{acot}^{2}{\left(5 x \right)} - 100 x \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)} - 310 \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)} + 10 \operatorname{acot}^{2}{\left(5 x \right)}}{250 x^{3} + 775 x^{2} + 10 x + 31}$$
(10*acot(5*x)^2 - 310*acot(5*x)*log(31/10 + x) + 250*x^2*acot(5*x)^2 - 100*x*acot(5*x)*log(31/10 + x))/(31 + 10*x + 250*x^3 + 775*x^2)
Denominador racional
[src]
2 /31 \ 2 2 /31 \
10*acot (5*x) - 310*acot(5*x)*log|-- + x| + 250*x *acot (5*x) - 100*x*acot(5*x)*log|-- + x|
\10 / \10 /
-------------------------------------------------------------------------------------------
/ 2\
\1 + 25*x /*(31 + 10*x)
$$\frac{250 x^{2} \operatorname{acot}^{2}{\left(5 x \right)} - 100 x \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)} - 310 \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)} + 10 \operatorname{acot}^{2}{\left(5 x \right)}}{\left(10 x + 31\right) \left(25 x^{2} + 1\right)}$$
(10*acot(5*x)^2 - 310*acot(5*x)*log(31/10 + x) + 250*x^2*acot(5*x)^2 - 100*x*acot(5*x)*log(31/10 + x))/((1 + 25*x^2)*(31 + 10*x))
Parte trigonométrica
[src]
/31 \
2 10*acot(5*x)*log|-- + x|
acot (5*x) \10 /
---------- - ------------------------
31 2
-- + x 1 + 25*x
10
$$- \frac{10 \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{x + \frac{31}{10}}$$
acot(5*x)^2/(31/10 + x) - 10*acot(5*x)*log(31/10 + x)/(1 + 25*x^2)
Potencias
[src]
/31 \
2 10*acot(5*x)*log|-- + x|
acot (5*x) \10 /
---------- - ------------------------
31 2
-- + x 1 + 25*x
10
$$- \frac{10 \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{x + \frac{31}{10}}$$
acot(5*x)^2/(31/10 + x) - 10*acot(5*x)*log(31/10 + x)/(1 + 25*x^2)
Unión de expresiones racionales
[src]
// 2\ /31 + 10*x\\
10*|\1 + 25*x /*acot(5*x) - (31 + 10*x)*log|---------||*acot(5*x)
\ \ 10 //
-----------------------------------------------------------------
/ 2\
\1 + 25*x /*(31 + 10*x)
$$\frac{10 \left(- \left(10 x + 31\right) \log{\left(\frac{10 x + 31}{10} \right)} + \left(25 x^{2} + 1\right) \operatorname{acot}{\left(5 x \right)}\right) \operatorname{acot}{\left(5 x \right)}}{\left(10 x + 31\right) \left(25 x^{2} + 1\right)}$$
10*((1 + 25*x^2)*acot(5*x) - (31 + 10*x)*log((31 + 10*x)/10))*acot(5*x)/((1 + 25*x^2)*(31 + 10*x))
Combinatoria
[src]
/ /31 \ /31 \ 2 \
10*|- 31*log|-- + x| - 10*x*log|-- + x| + 25*x *acot(5*x) + acot(5*x)|*acot(5*x)
\ \10 / \10 / /
--------------------------------------------------------------------------------
/ 2\
\1 + 25*x /*(31 + 10*x)
$$\frac{10 \left(25 x^{2} \operatorname{acot}{\left(5 x \right)} - 10 x \log{\left(x + \frac{31}{10} \right)} - 31 \log{\left(x + \frac{31}{10} \right)} + \operatorname{acot}{\left(5 x \right)}\right) \operatorname{acot}{\left(5 x \right)}}{\left(10 x + 31\right) \left(25 x^{2} + 1\right)}$$
10*(-31*log(31/10 + x) - 10*x*log(31/10 + x) + 25*x^2*acot(5*x) + acot(5*x))*acot(5*x)/((1 + 25*x^2)*(31 + 10*x))
Compilar la expresión
[src]
/ 31\
2 10*acot(5*x)*log|x + --|
acot (5*x) \ 10/
---------- - ------------------------
31 2
-- + x 1 + 25*x
10
$$- \frac{10 \log{\left(x + \frac{31}{10} \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{x + \frac{31}{10}}$$
acot(5*x)^2/(31/10 + x) - 10*acot(5*x)*log(x + 31/10)/(1 + 25*x^2)
Respuesta numérica
[src]
acot(5*x)^2/(3.1 + x) - 10.0*acot(5*x)*log(x + 31/10)/(1.0 + 25.0*x^2)
acot(5*x)^2/(3.1 + x) - 10.0*acot(5*x)*log(x + 31/10)/(1.0 + 25.0*x^2)