Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
pi*sin(n)/n-((n^2-2)*sin(n)+2*n*cos(n))/(pi*n^3)
¿Cómo vas a descomponer esta pi*sin(n)/n-((n^2-2)*sin(n)+2*n*cos(n))/(pi*n^3) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 \
pi*sin(n) \n - 2/*sin(n) + 2*n*cos(n)
--------- - ----------------------------
n 3
pi*n
$$- \frac{2 n \cos{\left(n \right)} + \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}} + \frac{\pi \sin{\left(n \right)}}{n}$$
(pi*sin(n))/n - ((n^2 - 2)*sin(n) + (2*n)*cos(n))/(pi*n^3)
Simplificación general
[src]
/ 2\ 2 2
\2 - n /*sin(n) - 2*n*cos(n) + pi *n *sin(n)
--------------------------------------------
3
pi*n
$$\frac{\pi^{2} n^{2} \sin{\left(n \right)} - 2 n \cos{\left(n \right)} + \left(2 - n^{2}\right) \sin{\left(n \right)}}{\pi n^{3}}$$
((2 - n^2)*sin(n) - 2*n*cos(n) + pi^2*n^2*sin(n))/(pi*n^3)
Respuesta numérica
[src]
3.14159265358979*sin(n)/n - 0.318309886183791*((-2.0 + n^2)*sin(n) + 2.0*n*cos(n))/n^3
3.14159265358979*sin(n)/n - 0.318309886183791*((-2.0 + n^2)*sin(n) + 2.0*n*cos(n))/n^3
Denominador racional
[src]
/ / 2\ \ 2 3
n*\- \-2 + n /*sin(n) - 2*n*cos(n)/ + pi *n *sin(n)
---------------------------------------------------
4
pi*n
$$\frac{\pi^{2} n^{3} \sin{\left(n \right)} + n \left(- 2 n \cos{\left(n \right)} - \left(n^{2} - 2\right) \sin{\left(n \right)}\right)}{\pi n^{4}}$$
(n*(-(-2 + n^2)*sin(n) - 2*n*cos(n)) + pi^2*n^3*sin(n))/(pi*n^4)
Unión de expresiones racionales
[src]
/ 2\ 2 2
- \-2 + n /*sin(n) - 2*n*cos(n) + pi *n *sin(n)
-----------------------------------------------
3
pi*n
$$\frac{\pi^{2} n^{2} \sin{\left(n \right)} - 2 n \cos{\left(n \right)} - \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
(-(-2 + n^2)*sin(n) - 2*n*cos(n) + pi^2*n^2*sin(n))/(pi*n^3)
Potencias
[src]
/ 2\
pi*sin(n) - \-2 + n /*sin(n) - 2*n*cos(n)
--------- + -------------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} + \frac{- 2 n \cos{\left(n \right)} - \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
/ 2\
pi*sin(n) \-2 + n /*sin(n) + 2*n*cos(n)
--------- - -----------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
/ I*n -I*n\ / 2\ / -I*n I*n\
|e e | I*\-2 + n /*\- e + e /
2*n*|---- + -----| - ---------------------------- / -I*n I*n\
\ 2 2 / 2 pi*I*\- e + e /
- ------------------------------------------------- - ---------------------
3 2*n
pi*n
$$- \frac{i \pi \left(e^{i n} - e^{- i n}\right)}{2 n} - \frac{2 n \left(\frac{e^{i n}}{2} + \frac{e^{- i n}}{2}\right) - \frac{i \left(n^{2} - 2\right) \left(e^{i n} - e^{- i n}\right)}{2}}{\pi n^{3}}$$
-(2*n*(exp(i*n)/2 + exp(-i*n)/2) - i*(-2 + n^2)*(-exp(-i*n) + exp(i*n))/2)/(pi*n^3) - pi*i*(-exp(-i*n) + exp(i*n))/(2*n)
Compilar la expresión
[src]
/ 2\
pi*sin(n) \-2 + n /*sin(n) + 2*n*cos(n)
--------- - -----------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
pi*sin(n)/n - ((-2 + n^2)*sin(n) + 2*n*cos(n))/(pi*n^3)
Denominador común
[src]
2 2 2
2*sin(n) - n *sin(n) - 2*n*cos(n) + pi *n *sin(n)
-------------------------------------------------
3
pi*n
$$\frac{- n^{2} \sin{\left(n \right)} + \pi^{2} n^{2} \sin{\left(n \right)} - 2 n \cos{\left(n \right)} + 2 \sin{\left(n \right)}}{\pi n^{3}}$$
(2*sin(n) - n^2*sin(n) - 2*n*cos(n) + pi^2*n^2*sin(n))/(pi*n^3)
Combinatoria
[src]
2 2 2
2*sin(n) - n *sin(n) - 2*n*cos(n) + pi *n *sin(n)
-------------------------------------------------
3
pi*n
$$\frac{- n^{2} \sin{\left(n \right)} + \pi^{2} n^{2} \sin{\left(n \right)} - 2 n \cos{\left(n \right)} + 2 \sin{\left(n \right)}}{\pi n^{3}}$$
(2*sin(n) - n^2*sin(n) - 2*n*cos(n) + pi^2*n^2*sin(n))/(pi*n^3)
Parte trigonométrica
[src]
/ 2 \
pi*sin(n) \n - 2/*sin(n) + 2*n*cos(n)
--------- - ----------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
2
-4 + 2*n 2*n
--------- + -----------
2*csc(n) /pi \
csc|-- - n|
pi \2 /
-------- - -----------------------
n*csc(n) 3
pi*n
$$\frac{\pi}{n \csc{\left(n \right)}} - \frac{\frac{2 n}{\csc{\left(- n + \frac{\pi}{2} \right)}} + \frac{2 n^{2} - 4}{2 \csc{\left(n \right)}}}{\pi n^{3}}$$
/ 2\
\-4 + 2*n /*sin(n)
------------------ + 2*n*cos(n)
pi*sin(n) 2
--------- - -------------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \frac{\left(2 n^{2} - 4\right) \sin{\left(n \right)}}{2}}{\pi n^{3}}$$
/ 2/n\\ / 2\ /n\
2*n*|1 - tan |-|| 2*\-2 + n /*tan|-|
\ \2// \2/
----------------- + ------------------
2/n\ 2/n\ /n\
1 + tan |-| 1 + tan |-| 2*pi*tan|-|
\2/ \2/ \2/
- -------------------------------------- + ---------------
3 / 2/n\\
pi*n n*|1 + tan |-||
\ \2//
$$\frac{2 \pi \tan{\left(\frac{n}{2} \right)}}{n \left(\tan^{2}{\left(\frac{n}{2} \right)} + 1\right)} - \frac{\frac{2 n \left(1 - \tan^{2}{\left(\frac{n}{2} \right)}\right)}{\tan^{2}{\left(\frac{n}{2} \right)} + 1} + \frac{2 \left(n^{2} - 2\right) \tan{\left(\frac{n}{2} \right)}}{\tan^{2}{\left(\frac{n}{2} \right)} + 1}}{\pi n^{3}}$$
2
-2 + n 2*n
------- + ------
pi csc(n) sec(n)
-------- - ----------------
n*csc(n) 3
pi*n
$$\frac{\pi}{n \csc{\left(n \right)}} - \frac{\frac{2 n}{\sec{\left(n \right)}} + \frac{n^{2} - 2}{\csc{\left(n \right)}}}{\pi n^{3}}$$
/ 2\ / pi\
\-4 + 2*n /*cos|n - --|
/ pi\ \ 2 /
pi*cos|n - --| ----------------------- + 2*n*cos(n)
\ 2 / 2
-------------- - ------------------------------------
n 3
pi*n
$$\frac{\pi \cos{\left(n - \frac{\pi}{2} \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \frac{\left(2 n^{2} - 4\right) \cos{\left(n - \frac{\pi}{2} \right)}}{2}}{\pi n^{3}}$$
/ 2/n\\ / 2\ /n\
2*n*|-1 + cot |-|| 2*\-2 + n /*cot|-|
\ \2// \2/
------------------ + ------------------
2/n\ 2/n\ /n\
1 + cot |-| 1 + cot |-| 2*pi*cot|-|
\2/ \2/ \2/
- --------------------------------------- + ---------------
3 / 2/n\\
pi*n n*|1 + cot |-||
\ \2//
$$\frac{2 \pi \cot{\left(\frac{n}{2} \right)}}{n \left(\cot^{2}{\left(\frac{n}{2} \right)} + 1\right)} - \frac{\frac{2 n \left(\cot^{2}{\left(\frac{n}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{n}{2} \right)} + 1} + \frac{2 \left(n^{2} - 2\right) \cot{\left(\frac{n}{2} \right)}}{\cot^{2}{\left(\frac{n}{2} \right)} + 1}}{\pi n^{3}}$$
2
-2 + n 2*n
------- + -----------
csc(n) /pi \
csc|-- - n|
pi \2 /
-------- - ---------------------
n*csc(n) 3
pi*n
$$\frac{\pi}{n \csc{\left(n \right)}} - \frac{\frac{2 n}{\csc{\left(- n + \frac{\pi}{2} \right)}} + \frac{n^{2} - 2}{\csc{\left(n \right)}}}{\pi n^{3}}$$
/ 2\ / pi\
\-2 + n /*sin(n) + 2*n*sin|n + --|
pi*sin(n) \ 2 /
--------- - ----------------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \sin{\left(n + \frac{\pi}{2} \right)} + \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
/ pi\ / 2\ / pi\
pi*cos|n - --| \-2 + n /*cos|n - --| + 2*n*cos(n)
\ 2 / \ 2 /
-------------- - ----------------------------------
n 3
pi*n
$$\frac{\pi \cos{\left(n - \frac{\pi}{2} \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \left(n^{2} - 2\right) \cos{\left(n - \frac{\pi}{2} \right)}}{\pi n^{3}}$$
/ 2\ /n\ / 2/n\\
\-4 + 2*n /*cot|-| 2*n*|-1 + cot |-||
\2/ \ \2//
------------------ + ------------------
2/n\ 2/n\ /n\
1 + cot |-| 1 + cot |-| 2*pi*cot|-|
\2/ \2/ \2/
- --------------------------------------- + ---------------
3 / 2/n\\
pi*n n*|1 + cot |-||
\ \2//
$$\frac{2 \pi \cot{\left(\frac{n}{2} \right)}}{n \left(\cot^{2}{\left(\frac{n}{2} \right)} + 1\right)} - \frac{\frac{2 n \left(\cot^{2}{\left(\frac{n}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{n}{2} \right)} + 1} + \frac{\left(2 n^{2} - 4\right) \cot{\left(\frac{n}{2} \right)}}{\cot^{2}{\left(\frac{n}{2} \right)} + 1}}{\pi n^{3}}$$
2
-4 + 2*n 2*n
------------- + ------
/ pi\ sec(n)
2*sec|n - --|
pi \ 2 /
------------- - ----------------------
/ pi\ 3
n*sec|n - --| pi*n
\ 2 /
$$\frac{\pi}{n \sec{\left(n - \frac{\pi}{2} \right)}} - \frac{\frac{2 n}{\sec{\left(n \right)}} + \frac{2 n^{2} - 4}{2 \sec{\left(n - \frac{\pi}{2} \right)}}}{\pi n^{3}}$$
/ 2\
pi*sin(n) \-2 + n /*sin(n) + 2*n*cos(n)
--------- - -----------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \cos{\left(n \right)} + \left(n^{2} - 2\right) \sin{\left(n \right)}}{\pi n^{3}}$$
2
-2 + n 2*n
----------- + ------
/ pi\ sec(n)
sec|n - --|
pi \ 2 /
------------- - --------------------
/ pi\ 3
n*sec|n - --| pi*n
\ 2 /
$$\frac{\pi}{n \sec{\left(n - \frac{\pi}{2} \right)}} - \frac{\frac{2 n}{\sec{\left(n \right)}} + \frac{n^{2} - 2}{\sec{\left(n - \frac{\pi}{2} \right)}}}{\pi n^{3}}$$
/ 2\
\-4 + 2*n /*sin(n) / pi\
------------------ + 2*n*sin|n + --|
pi*sin(n) 2 \ 2 /
--------- - ------------------------------------
n 3
pi*n
$$\frac{\pi \sin{\left(n \right)}}{n} - \frac{2 n \sin{\left(n + \frac{\pi}{2} \right)} + \frac{\left(2 n^{2} - 4\right) \sin{\left(n \right)}}{2}}{\pi n^{3}}$$
/ 2\ /n\ / 2/n\\
\-4 + 2*n /*tan|-| 2*n*|1 - tan |-||
\2/ \ \2//
------------------ + -----------------
2/n\ 2/n\ /n\
1 + tan |-| 1 + tan |-| 2*pi*tan|-|
\2/ \2/ \2/
- -------------------------------------- + ---------------
3 / 2/n\\
pi*n n*|1 + tan |-||
\ \2//
$$\frac{2 \pi \tan{\left(\frac{n}{2} \right)}}{n \left(\tan^{2}{\left(\frac{n}{2} \right)} + 1\right)} - \frac{\frac{2 n \left(1 - \tan^{2}{\left(\frac{n}{2} \right)}\right)}{\tan^{2}{\left(\frac{n}{2} \right)} + 1} + \frac{\left(2 n^{2} - 4\right) \tan{\left(\frac{n}{2} \right)}}{\tan^{2}{\left(\frac{n}{2} \right)} + 1}}{\pi n^{3}}$$
-((-4 + 2*n^2)*tan(n/2)/(1 + tan(n/2)^2) + 2*n*(1 - tan(n/2)^2)/(1 + tan(n/2)^2))/(pi*n^3) + 2*pi*tan(n/2)/(n*(1 + tan(n/2)^2))