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Simplificación de expresiones/
Descomposición en fracciones simples/
acot(x^3)^2/(x+13/10)-6*x^2*acot(x^3)*log(x+13/10)/(1+x^6)
¿Cómo vas a descomponer esta acot(x^3)^2/(x+13/10)-6*x^2*acot(x^3)*log(x+13/10)/(1+x^6) expresión en fracciones?
Solución
Ha introducido
[src]
2 / 3\ / 13\
2/ 3\ 6*x *acot\x /*log|x + --|
acot \x / \ 10/
--------- - -------------------------
13 6
x + -- 1 + x
10
$$- \frac{6 x^{2} \operatorname{acot}{\left(x^{3} \right)} \log{\left(x + \frac{13}{10} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}}$$
acot(x^3)^2/(x + 13/10) - ((6*x^2)*acot(x^3))*log(x + 13/10)/(1 + x^6)
Simplificación general
[src]
/ / 6\ / 3\ 2 /13 \\ / 3\
2*|5*\1 + x /*acot\x / - 3*x *(13 + 10*x)*log|-- + x||*acot\x /
\ \10 //
---------------------------------------------------------------
/ 6\
\1 + x /*(13 + 10*x)
$$\frac{2 \left(- 3 x^{2} \left(10 x + 13\right) \log{\left(x + \frac{13}{10} \right)} + 5 \left(x^{6} + 1\right) \operatorname{acot}{\left(x^{3} \right)}\right) \operatorname{acot}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{6} + 1\right)}$$
2*(5*(1 + x^6)*acot(x^3) - 3*x^2*(13 + 10*x)*log(13/10 + x))*acot(x^3)/((1 + x^6)*(13 + 10*x))
Respuesta numérica
[src]
acot(x^3)^2/(1.3 + x) - 6.0*x^2*acot(x^3)*log(x + 13/10)/(1.0 + x^6)
acot(x^3)^2/(1.3 + x) - 6.0*x^2*acot(x^3)*log(x + 13/10)/(1.0 + x^6)
Denominador racional
[src]
2/ 3\ 6 2/ 3\ 2 / 3\ /13 \ 3 / 3\ /13 \
10*acot \x / + 10*x *acot \x / - 78*x *acot\x /*log|-- + x| - 60*x *acot\x /*log|-- + x|
\10 / \10 /
----------------------------------------------------------------------------------------
/ 6\
\1 + x /*(13 + 10*x)
$$\frac{10 x^{6} \operatorname{acot}^{2}{\left(x^{3} \right)} - 60 x^{3} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} - 78 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} + 10 \operatorname{acot}^{2}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{6} + 1\right)}$$
(10*acot(x^3)^2 + 10*x^6*acot(x^3)^2 - 78*x^2*acot(x^3)*log(13/10 + x) - 60*x^3*acot(x^3)*log(13/10 + x))/((1 + x^6)*(13 + 10*x))
Unión de expresiones racionales
[src]
/ / 6\ / 3\ 2 /13 + 10*x\\ / 3\
2*|5*\1 + x /*acot\x / - 3*x *(13 + 10*x)*log|---------||*acot\x /
\ \ 10 //
------------------------------------------------------------------
/ 6\
\1 + x /*(13 + 10*x)
$$\frac{2 \left(- 3 x^{2} \left(10 x + 13\right) \log{\left(\frac{10 x + 13}{10} \right)} + 5 \left(x^{6} + 1\right) \operatorname{acot}{\left(x^{3} \right)}\right) \operatorname{acot}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{6} + 1\right)}$$
2*(5*(1 + x^6)*acot(x^3) - 3*x^2*(13 + 10*x)*log((13 + 10*x)/10))*acot(x^3)/((1 + x^6)*(13 + 10*x))
Potencias
[src]
2 / 3\ /13 \
2/ 3\ 6*x *acot\x /*log|-- + x|
acot \x / \10 /
--------- - -------------------------
13 6
-- + x 1 + x
10
$$- \frac{6 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}}$$
acot(x^3)^2/(13/10 + x) - 6*x^2*acot(x^3)*log(13/10 + x)/(1 + x^6)
Parte trigonométrica
[src]
2 / 3\ /13 \
2/ 3\ 6*x *acot\x /*log|-- + x|
acot \x / \10 /
--------- - -------------------------
13 6
-- + x 1 + x
10
$$- \frac{6 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}}$$
acot(x^3)^2/(13/10 + x) - 6*x^2*acot(x^3)*log(13/10 + x)/(1 + x^6)
Denominador común
[src]
2/ 3\ 6 2/ 3\ 2 / 3\ /13 \ 3 / 3\ /13 \
10*acot \x / + 10*x *acot \x / - 78*x *acot\x /*log|-- + x| - 60*x *acot\x /*log|-- + x|
\10 / \10 /
----------------------------------------------------------------------------------------
7 6
13 + 10*x + 10*x + 13*x
$$\frac{10 x^{6} \operatorname{acot}^{2}{\left(x^{3} \right)} - 60 x^{3} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} - 78 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} + 10 \operatorname{acot}^{2}{\left(x^{3} \right)}}{10 x^{7} + 13 x^{6} + 10 x + 13}$$
(10*acot(x^3)^2 + 10*x^6*acot(x^3)^2 - 78*x^2*acot(x^3)*log(13/10 + x) - 60*x^3*acot(x^3)*log(13/10 + x))/(13 + 10*x + 10*x^7 + 13*x^6)
Combinatoria
[src]
/ / 3\ 2 /13 \ 3 /13 \ 6 / 3\\ / 3\
2*|5*acot\x / - 39*x *log|-- + x| - 30*x *log|-- + x| + 5*x *acot\x /|*acot\x /
\ \10 / \10 / /
-------------------------------------------------------------------------------
/ 2\ / 4 2\
\1 + x /*(13 + 10*x)*\1 + x - x /
$$\frac{2 \left(5 x^{6} \operatorname{acot}{\left(x^{3} \right)} - 30 x^{3} \log{\left(x + \frac{13}{10} \right)} - 39 x^{2} \log{\left(x + \frac{13}{10} \right)} + 5 \operatorname{acot}{\left(x^{3} \right)}\right) \operatorname{acot}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{2} + 1\right) \left(x^{4} - x^{2} + 1\right)}$$
2*(5*acot(x^3) - 39*x^2*log(13/10 + x) - 30*x^3*log(13/10 + x) + 5*x^6*acot(x^3))*acot(x^3)/((1 + x^2)*(13 + 10*x)*(1 + x^4 - x^2))
Compilar la expresión
[src]
2 / 3\ / 13\
2/ 3\ 6*x *acot\x /*log|x + --|
acot \x / \ 10/
--------- - -------------------------
13 6
-- + x 1 + x
10
$$- \frac{6 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}}$$
acot(x^3)^2/(13/10 + x) - 6*x^2*acot(x^3)*log(x + 13/10)/(1 + x^6)