Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+2*x+3)-atan((2*x+2)/2^(3/2))/sqrt(2)-2/(2+x)
¿Cómo vas a descomponer esta log(x^2+2*x+3)-atan((2*x+2)/2^(3/2))/sqrt(2)-2/(2+x) expresión en fracciones?
Solución
Ha introducido
[src]
/2*x + 2\
atan|-------|
| 3/2 |
/ 2 \ \ 2 / 2
log\x + 2*x + 3/ - ------------- - -----
___ 2 + x
\/ 2
$$\left(\log{\left(\left(x^{2} + 2 x\right) + 3 \right)} - \frac{\operatorname{atan}{\left(\frac{2 x + 2}{2^{\frac{3}{2}}} \right)}}{\sqrt{2}}\right) - \frac{2}{x + 2}$$
log(x^2 + 2*x + 3) - atan((2*x + 2)/2^(3/2))/sqrt(2) - 2/(2 + x)
Simplificación general
[src]
/ / ___ \\
| / 2 \ ___ |\/ 2 *(1 + x)||
-4 + (2 + x)*|2*log\3 + x + 2*x/ - \/ 2 *atan|-------------||
\ \ 2 //
--------------------------------------------------------------
2*(2 + x)
$$\frac{\left(x + 2\right) \left(2 \log{\left(x^{2} + 2 x + 3 \right)} - \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(x + 1\right)}{2} \right)}\right) - 4}{2 \left(x + 2\right)}$$
(-4 + (2 + x)*(2*log(3 + x^2 + 2*x) - sqrt(2)*atan(sqrt(2)*(1 + x)/2)))/(2*(2 + x))
Respuesta numérica
[src]
-2.0/(2.0 + x) - 0.707106781186547*atan((2*x + 2)/2^(3/2)) + log(x^2 + 2*x + 3)
-2.0/(2.0 + x) - 0.707106781186547*atan((2*x + 2)/2^(3/2)) + log(x^2 + 2*x + 3)
Denominador racional
[src]
/ ___ ___\ / ___ ___\
/ 2 \ ___ |\/ 2 x*\/ 2 | / 2 \ ___ |\/ 2 x*\/ 2 |
-4 + 4*log\3 + x + 2*x/ - 2*\/ 2 *atan|----- + -------| + 2*x*log\3 + x + 2*x/ - x*\/ 2 *atan|----- + -------|
\ 2 2 / \ 2 2 /
----------------------------------------------------------------------------------------------------------------
4 + 2*x
$$\frac{2 x \log{\left(x^{2} + 2 x + 3 \right)} - \sqrt{2} x \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)} + 4 \log{\left(x^{2} + 2 x + 3 \right)} - 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)} - 4}{2 x + 4}$$
(-4 + 4*log(3 + x^2 + 2*x) - 2*sqrt(2)*atan(sqrt(2)/2 + x*sqrt(2)/2) + 2*x*log(3 + x^2 + 2*x) - x*sqrt(2)*atan(sqrt(2)/2 + x*sqrt(2)/2))/(4 + 2*x)
Denominador común
[src]
/ ___ ___\
___ |\/ 2 x*\/ 2 |
\/ 2 *atan|----- + -------|
2 \ 2 2 / / 2 \
- ----- - --------------------------- + log\3 + x + 2*x/
2 + x 2
$$\log{\left(x^{2} + 2 x + 3 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)}}{2} - \frac{2}{x + 2}$$
-2/(2 + x) - sqrt(2)*atan(sqrt(2)/2 + x*sqrt(2)/2)/2 + log(3 + x^2 + 2*x)
Potencias
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___ / ___ /1 x\\
\/ 2 *atan|\/ 2 *|- + -||
2 \ \2 2// / 2 \
- ----- - ------------------------- + log\3 + x + 2*x/
2 + x 2
$$\log{\left(x^{2} + 2 x + 3 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \left(\frac{x}{2} + \frac{1}{2}\right) \right)}}{2} - \frac{2}{x + 2}$$
/ ___ \
___ |\/ 2 *(2 + 2*x)|
\/ 2 *atan|---------------|
2 \ 4 / / 2 \
- ----- - --------------------------- + log\3 + x + 2*x/
2 + x 2
$$\log{\left(x^{2} + 2 x + 3 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(2 x + 2\right)}{4} \right)}}{2} - \frac{2}{x + 2}$$
-2/(2 + x) - sqrt(2)*atan(sqrt(2)*(2 + 2*x)/4)/2 + log(3 + x^2 + 2*x)
Combinatoria
[src]
/ / ___ ___\ / ___ ___\\
| / 2 \ / 2 \ ___ |\/ 2 x*\/ 2 | ___ |\/ 2 x*\/ 2 ||
-|4 - 4*log\3 + x + 2*x/ - 2*x*log\3 + x + 2*x/ + 2*\/ 2 *atan|----- + -------| + x*\/ 2 *atan|----- + -------||
\ \ 2 2 / \ 2 2 //
-------------------------------------------------------------------------------------------------------------------
2*(2 + x)
$$- \frac{- 2 x \log{\left(x^{2} + 2 x + 3 \right)} + \sqrt{2} x \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)} - 4 \log{\left(x^{2} + 2 x + 3 \right)} + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)} + 4}{2 \left(x + 2\right)}$$
-(4 - 4*log(3 + x^2 + 2*x) - 2*x*log(3 + x^2 + 2*x) + 2*sqrt(2)*atan(sqrt(2)/2 + x*sqrt(2)/2) + x*sqrt(2)*atan(sqrt(2)/2 + x*sqrt(2)/2))/(2*(2 + x))
Compilar la expresión
[src]
___ /2*x + 2\
\/ 2 *atan|-------|
| 3/2 |
2 \ 2 / / 2 \
- ----- - ------------------- + log\x + 2*x + 3/
2 + x 2
$$\log{\left(\left(x^{2} + 2 x\right) + 3 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{2 x + 2}{2^{\frac{3}{2}}} \right)}}{2} - \frac{2}{x + 2}$$
-2/(2 + x) - sqrt(2)*atan((2*x + 2)/2^(3/2))/2 + log(x^2 + 2*x + 3)
Parte trigonométrica
[src]
/ ___ \
___ |\/ 2 *(2 + 2*x)|
\/ 2 *atan|---------------|
2 \ 4 / / 2 \
- ----- - --------------------------- + log\3 + x + 2*x/
2 + x 2
$$\log{\left(x^{2} + 2 x + 3 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(2 x + 2\right)}{4} \right)}}{2} - \frac{2}{x + 2}$$
-2/(2 + x) - sqrt(2)*atan(sqrt(2)*(2 + 2*x)/4)/2 + log(3 + x^2 + 2*x)
Unión de expresiones racionales
[src]
/ / ___ \\
| ___ |\/ 2 *(1 + x)||
-4 + (2 + x)*|2*log(3 + x*(2 + x)) - \/ 2 *atan|-------------||
\ \ 2 //
---------------------------------------------------------------
2*(2 + x)
$$\frac{\left(x + 2\right) \left(2 \log{\left(x \left(x + 2\right) + 3 \right)} - \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(x + 1\right)}{2} \right)}\right) - 4}{2 \left(x + 2\right)}$$
(-4 + (2 + x)*(2*log(3 + x*(2 + x)) - sqrt(2)*atan(sqrt(2)*(1 + x)/2)))/(2*(2 + x))