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Simplificación de expresiones/
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log(x^2+2*x+6)/2-atan((2*x+2)/(2*sqrt(5)))/sqrt(5)
¿Cómo vas a descomponer esta log(x^2+2*x+6)/2-atan((2*x+2)/(2*sqrt(5)))/sqrt(5) expresión en fracciones?
Solución
Ha introducido
[src]
/2*x + 2\
atan|-------|
/ 2 \ | ___|
log\x + 2*x + 6/ \2*\/ 5 /
----------------- - -------------
2 ___
\/ 5
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 6 \right)}}{2} - \frac{\operatorname{atan}{\left(\frac{2 x + 2}{2 \sqrt{5}} \right)}}{\sqrt{5}}$$
log(x^2 + 2*x + 6)/2 - atan((2*x + 2)/((2*sqrt(5))))/sqrt(5)
Simplificación general
[src]
/ ___ \
___ |\/ 5 *(1 + x)|
/ 2 \ \/ 5 *atan|-------------|
log\6 + x + 2*x/ \ 5 /
----------------- - -------------------------
2 5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(x + 1\right)}{5} \right)}}{5}$$
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)*(1 + x)/5)/5
Respuesta numérica
[src]
0.5*log(x^2 + 2*x + 6) - 0.447213595499958*atan((2*x + 2)/((2*sqrt(5))))
0.5*log(x^2 + 2*x + 6) - 0.447213595499958*atan((2*x + 2)/((2*sqrt(5))))
Parte trigonométrica
[src]
/ ___ \
___ |\/ 5 *(2 + 2*x)|
/ 2 \ \/ 5 *atan|---------------|
log\6 + x + 2*x/ \ 10 /
----------------- - ---------------------------
2 5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 2\right)}{10} \right)}}{5}$$
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)*(2 + 2*x)/10)/5
Denominador racional
[src]
/ ___ ___\
/ 2 \ ___ |\/ 5 x*\/ 5 |
5*log\6 + x + 2*x/ - 2*\/ 5 *atan|----- + -------|
\ 5 5 /
---------------------------------------------------
10
$$\frac{5 \log{\left(x^{2} + 2 x + 6 \right)} - 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \right)}}{10}$$
(5*log(6 + x^2 + 2*x) - 2*sqrt(5)*atan(sqrt(5)/5 + x*sqrt(5)/5))/10
Potencias
[src]
___ / ___ /1 x\\
/ 2 \ \/ 5 *atan|\/ 5 *|- + -||
log\6 + x + 2*x/ \ \5 5//
----------------- - -------------------------
2 5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} \left(\frac{x}{5} + \frac{1}{5}\right) \right)}}{5}$$
/ ___ \
___ |\/ 5 *(2 + 2*x)|
/ 2 \ \/ 5 *atan|---------------|
log\6 + x + 2*x/ \ 10 /
----------------- - ---------------------------
2 5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 2\right)}{10} \right)}}{5}$$
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)*(2 + 2*x)/10)/5
Denominador común
[src]
/ ___ ___\
___ |\/ 5 x*\/ 5 |
/ 2 \ \/ 5 *atan|----- + -------|
log\6 + x + 2*x/ \ 5 5 /
----------------- - ---------------------------
2 5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \right)}}{5}$$
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)/5 + x*sqrt(5)/5)/5
Combinatoria
[src]
/ ___ ___\
___ |\/ 5 x*\/ 5 |
/ 2 \ \/ 5 *atan|----- + -------|
log\6 + x + 2*x/ \ 5 5 /
----------------- - ---------------------------
2 5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \right)}}{5}$$
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)/5 + x*sqrt(5)/5)/5
Unión de expresiones racionales
[src]
/ ___ \
___ |\/ 5 *(1 + x)|
5*log(6 + x*(2 + x)) - 2*\/ 5 *atan|-------------|
\ 5 /
--------------------------------------------------
10
$$\frac{5 \log{\left(x \left(x + 2\right) + 6 \right)} - 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(x + 1\right)}{5} \right)}}{10}$$
(5*log(6 + x*(2 + x)) - 2*sqrt(5)*atan(sqrt(5)*(1 + x)/5))/10
Compilar la expresión
[src]
___ /2*x + 2\
\/ 5 *atan|-------|
/ 2 \ | ___|
log\x + 2*x + 6/ \2*\/ 5 /
----------------- - -------------------
2 5
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 x + 2}{2 \sqrt{5}} \right)}}{5}$$
log(x^2 + 2*x + 6)/2 - sqrt(5)*atan((2*x + 2)/((2*sqrt(5))))/5