Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(a*atan(x))/((1+e^(pi*x))*(1+x^2)^(a/2))
¿Cómo vas a descomponer esta sin(a*atan(x))/((1+e^(pi*x))*(1+x^2)^(a/2)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(a*atan(x))
---------------------
a
-
2
/ pi*x\ / 2\
\1 + E /*\1 + x /
$$\frac{\sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{\left(e^{\pi x} + 1\right) \left(x^{2} + 1\right)^{\frac{a}{2}}}$$
sin(a*atan(x))/(((1 + E^(pi*x))*(1 + x^2)^(a/2)))
Simplificación general
[src]
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
--------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
(1 + x^2)^(-a/2)*sin(a*atan(x))/(1 + exp(pi*x))
Respuesta numérica
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(1.0 + x^2)^(-0.5*a)*sin(a*atan(x))/(1.0 + 2.71828182845905^(3.14159265358979*x))
(1.0 + x^2)^(-0.5*a)*sin(a*atan(x))/(1.0 + 2.71828182845905^(3.14159265358979*x))
Denominador común
[src]
sin(a*atan(x))
---------------------------
a a
- -
2 2
/ 2\ / 2\ pi*x
\1 + x / + \1 + x / *e
$$\frac{\sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{\frac{a}{2}} e^{\pi x} + \left(x^{2} + 1\right)^{\frac{a}{2}}}$$
sin(a*atan(x))/((1 + x^2)^(a/2) + (1 + x^2)^(a/2)*exp(pi*x))
Combinatoria
[src]
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
--------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
(1 + x^2)^(-a/2)*sin(a*atan(x))/(1 + exp(pi*x))
Unión de expresiones racionales
[src]
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
--------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
(1 + x^2)^(-a/2)*sin(a*atan(x))/(1 + exp(pi*x))
Potencias
[src]
-a
---
2
/ 2\ / -I*a*atan(x) I*a*atan(x)\
-I*\1 + x / *\- e + e /
------------------------------------------------
/ pi*x\
2*\1 + e /
$$- \frac{i \left(x^{2} + 1\right)^{- \frac{a}{2}} \left(e^{i a \operatorname{atan}{\left(x \right)}} - e^{- i a \operatorname{atan}{\left(x \right)}}\right)}{2 \left(e^{\pi x} + 1\right)}$$
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
--------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
(1 + x^2)^(-a/2)*sin(a*atan(x))/(1 + exp(pi*x))
Compilar la expresión
[src]
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
--------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
(1 + x^2)^(-a/2)*sin(a*atan(x))/(1 + exp(pi*x))
Denominador racional
[src]
___________
/ a -a
/ / 2\ / 2\
\/ \1 + x / *\1 + x / *sin(a*atan(x))
-----------------------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- a} \sqrt{\left(x^{2} + 1\right)^{a}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
sqrt((1 + x^2)^a)*(1 + x^2)^(-a)*sin(a*atan(x))/(1 + exp(pi*x))
Parte trigonométrica
[src]
-a
---
2
/ 2\ /a*atan(x)\
2*\1 + x / *tan|---------|
\ 2 /
---------------------------------
/ 2/a*atan(x)\\ / pi*x\
|1 + tan |---------||*\1 + e /
\ \ 2 //
$$\frac{2 \left(x^{2} + 1\right)^{- \frac{a}{2}} \tan{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)}}{\left(e^{\pi x} + 1\right) \left(\tan^{2}{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)} + 1\right)}$$
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
---------------------------
1 + cosh(pi*x) + sinh(pi*x)
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{\sinh{\left(\pi x \right)} + \cosh{\left(\pi x \right)} + 1}$$
-a
---
2
/ 2\
\1 + x /
--------------------------
/ pi*x\
\1 + e /*csc(a*atan(x))
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}}}{\left(e^{\pi x} + 1\right) \csc{\left(a \operatorname{atan}{\left(x \right)} \right)}}$$
-a
---
2
/ 2\ / pi \
\1 + x / *cos|- -- + a*atan(x)|
\ 2 /
---------------------------------
pi*x
1 + (cosh(1) + sinh(1))
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \cos{\left(a \operatorname{atan}{\left(x \right)} - \frac{\pi}{2} \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{\pi x} + 1}$$
-a
---
2
/ 2\ /a*atan(x)\
2*\1 + x / *tan|---------|
\ 2 /
---------------------------------------------------
/ pi*x\ / 2/a*atan(x)\\
\1 + (cosh(1) + sinh(1)) /*|1 + tan |---------||
\ \ 2 //
$$\frac{2 \left(x^{2} + 1\right)^{- \frac{a}{2}} \tan{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{\pi x} + 1\right) \left(\tan^{2}{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)} + 1\right)}$$
-a
---
2
/ 2\ /a*atan(x)\
2*\1 + x / *cot|---------|
\ 2 /
---------------------------------
/ 2/a*atan(x)\\ / pi*x\
|1 + cot |---------||*\1 + e /
\ \ 2 //
$$\frac{2 \left(x^{2} + 1\right)^{- \frac{a}{2}} \cot{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)}}{\left(e^{\pi x} + 1\right) \left(\cot^{2}{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)} + 1\right)}$$
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
---------------------------
pi*x
1 + (cosh(1) + sinh(1))
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{\pi x} + 1}$$
-a
---
2
/ 2\
\1 + x /
-----------*sin(a*atan(x))
pi*x
1 + E
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}}}{e^{\pi x} + 1} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}$$
-a
---
2
/ 2\
\1 + x /
---------------------------------
/ pi*x\ / pi \
\1 + e /*sec|- -- + a*atan(x)|
\ 2 /
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}}}{\left(e^{\pi x} + 1\right) \sec{\left(a \operatorname{atan}{\left(x \right)} - \frac{\pi}{2} \right)}}$$
-a
---
2
/ 2\
\1 + x /
---------------------------------------------------
/ pi*x\ / pi \
\1 + (cosh(1) + sinh(1)) /*sec|- -- + a*atan(x)|
\ 2 /
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{\pi x} + 1\right) \sec{\left(a \operatorname{atan}{\left(x \right)} - \frac{\pi}{2} \right)}}$$
-a
---
2
/ 2\
\1 + x / *sin(a*atan(x))
--------------------------
pi*x
1 + e
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \sin{\left(a \operatorname{atan}{\left(x \right)} \right)}}{e^{\pi x} + 1}$$
-a
---
2
/ 2\ /a*atan(x)\
2*\1 + x / *cot|---------|
\ 2 /
---------------------------------------------------
/ pi*x\ / 2/a*atan(x)\\
\1 + (cosh(1) + sinh(1)) /*|1 + cot |---------||
\ \ 2 //
$$\frac{2 \left(x^{2} + 1\right)^{- \frac{a}{2}} \cot{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{\pi x} + 1\right) \left(\cot^{2}{\left(\frac{a \operatorname{atan}{\left(x \right)}}{2} \right)} + 1\right)}$$
-a
---
2
/ 2\ / pi \
\1 + x / *cos|- -- + a*atan(x)|
\ 2 /
---------------------------------
1 + cosh(pi*x) + sinh(pi*x)
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}} \cos{\left(a \operatorname{atan}{\left(x \right)} - \frac{\pi}{2} \right)}}{\sinh{\left(\pi x \right)} + \cosh{\left(\pi x \right)} + 1}$$
-a
---
2
/ 2\
\1 + x /
--------------------------------------------
/ pi*x\
\1 + (cosh(1) + sinh(1)) /*csc(a*atan(x))
$$\frac{\left(x^{2} + 1\right)^{- \frac{a}{2}}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{\pi x} + 1\right) \csc{\left(a \operatorname{atan}{\left(x \right)} \right)}}$$
(1 + x^2)^(-a/2)/((1 + (cosh(1) + sinh(1))^(pi*x))*csc(a*atan(x)))