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Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2-x+1)/2+(7*atan((2*x-1)/sqrt(3)))/sqrt(3)+3/(1+x)
¿Cómo vas a descomponer esta log(x^2-x+1)/2+(7*atan((2*x-1)/sqrt(3)))/sqrt(3)+3/(1+x) expresión en fracciones?
Solución
Ha introducido
[src]
/2*x - 1\
7*atan|-------|
/ 2 \ | ___ |
log\x - x + 1/ \ \/ 3 / 3
--------------- + --------------- + -----
2 ___ 1 + x
\/ 3
$$\left(\frac{\log{\left(\left(x^{2} - x\right) + 1 \right)}}{2} + \frac{7 \operatorname{atan}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{\sqrt{3}}\right) + \frac{3}{x + 1}$$
log(x^2 - x + 1)/2 + (7*atan((2*x - 1)/sqrt(3)))/sqrt(3) + 3/(1 + x)
Simplificación general
[src]
/ / ___ \\
| / 2 \ ___ |\/ 3 *(-1 + 2*x)||
18 + (1 + x)*|3*log\1 + x - x/ + 14*\/ 3 *atan|----------------||
\ \ 3 //
------------------------------------------------------------------
6*(1 + x)
$$\frac{\left(x + 1\right) \left(3 \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}\right) + 18}{6 \left(x + 1\right)}$$
(18 + (1 + x)*(3*log(1 + x^2 - x) + 14*sqrt(3)*atan(sqrt(3)*(-1 + 2*x)/3)))/(6*(1 + x))
Denominador común
[src]
/ ___ ___\
___ | \/ 3 2*x*\/ 3 |
/ 2 \ 7*\/ 3 *atan|- ----- + ---------|
log\1 + x - x/ 3 \ 3 3 /
--------------- + ----- + ---------------------------------
2 1 + x 3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3} + \frac{3}{x + 1}$$
log(1 + x^2 - x)/2 + 3/(1 + x) + 7*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3)/3
Combinatoria
[src]
/ ___ ___\ / ___ ___\
/ 2 \ / 2 \ ___ | \/ 3 2*x*\/ 3 | ___ | \/ 3 2*x*\/ 3 |
18 + 3*log\1 + x - x/ + 3*x*log\1 + x - x/ + 14*\/ 3 *atan|- ----- + ---------| + 14*x*\/ 3 *atan|- ----- + ---------|
\ 3 3 / \ 3 3 /
------------------------------------------------------------------------------------------------------------------------
6*(1 + x)
$$\frac{3 x \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} x \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 3 \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 18}{6 \left(x + 1\right)}$$
(18 + 3*log(1 + x^2 - x) + 3*x*log(1 + x^2 - x) + 14*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3) + 14*x*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3))/(6*(1 + x))
Unión de expresiones racionales
[src]
/ / ___ \\
| ___ |\/ 3 *(-1 + 2*x)||
18 + (1 + x)*|3*log(1 + x*(-1 + x)) + 14*\/ 3 *atan|----------------||
\ \ 3 //
----------------------------------------------------------------------
6*(1 + x)
$$\frac{\left(x + 1\right) \left(3 \log{\left(x \left(x - 1\right) + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}\right) + 18}{6 \left(x + 1\right)}$$
(18 + (1 + x)*(3*log(1 + x*(-1 + x)) + 14*sqrt(3)*atan(sqrt(3)*(-1 + 2*x)/3)))/(6*(1 + x))
Denominador racional
[src]
/ ___ ___\ / ___ ___\
/ 2 \ / 2 \ ___ | \/ 3 2*x*\/ 3 | ___ | \/ 3 2*x*\/ 3 |
18 + 3*log\1 + x - x/ + 3*x*log\1 + x - x/ + 14*\/ 3 *atan|- ----- + ---------| + 14*x*\/ 3 *atan|- ----- + ---------|
\ 3 3 / \ 3 3 /
------------------------------------------------------------------------------------------------------------------------
6 + 6*x
$$\frac{3 x \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} x \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 3 \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 18}{6 x + 6}$$
(18 + 3*log(1 + x^2 - x) + 3*x*log(1 + x^2 - x) + 14*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3) + 14*x*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3))/(6 + 6*x)
Parte trigonométrica
[src]
/ ___ \
___ |\/ 3 *(-1 + 2*x)|
/ 2 \ 7*\/ 3 *atan|----------------|
log\1 + x - x/ 3 \ 3 /
--------------- + ----- + ------------------------------
2 1 + x 3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{3} + \frac{3}{x + 1}$$
log(1 + x^2 - x)/2 + 3/(1 + x) + 7*sqrt(3)*atan(sqrt(3)*(-1 + 2*x)/3)/3
Compilar la expresión
[src]
___ /2*x - 1\
7*\/ 3 *atan|-------|
/ 2 \ | ___ |
log\x - x + 1/ 3 \ \/ 3 /
--------------- + ----- + ---------------------
2 1 + x 3
$$\frac{\log{\left(\left(x^{2} - x\right) + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{3} + \frac{3}{x + 1}$$
log(x^2 - x + 1)/2 + 3/(1 + x) + 7*sqrt(3)*atan((2*x - 1)/sqrt(3))/3
Respuesta numérica
[src]
0.5*log(x^2 - x + 1) + 3.0/(1.0 + x) + 4.04145188432738*atan((2*x - 1)/sqrt(3))
0.5*log(x^2 - x + 1) + 3.0/(1.0 + x) + 4.04145188432738*atan((2*x - 1)/sqrt(3))
Potencias
[src]
/ ___ \
___ |\/ 3 *(-1 + 2*x)|
/ 2 \ 7*\/ 3 *atan|----------------|
log\1 + x - x/ 3 \ 3 /
--------------- + ----- + ------------------------------
2 1 + x 3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{3} + \frac{3}{x + 1}$$
___ / ___ / 1 2*x\\
/ 2 \ 7*\/ 3 *atan|\/ 3 *|- - + ---||
log\1 + x - x/ 3 \ \ 3 3 //
--------------- + ----- + -------------------------------
2 1 + x 3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{2 x}{3} - \frac{1}{3}\right) \right)}}{3} + \frac{3}{x + 1}$$
log(1 + x^2 - x)/2 + 3/(1 + x) + 7*sqrt(3)*atan(sqrt(3)*(-1/3 + 2*x/3))/3