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Simplificación de expresiones/ Descomposición en fracciones simples/ ln(3/sin(n/(n^3+1)))/ln(n)

¿Cómo vas a descomponer esta ln(3/sin(n/(n^3+1)))/ln(n) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /     3     \
log|-----------|
   |   /  n   \|
   |sin|------||
   |   | 3    ||
   \   \n  + 1//
----------------
     log(n)
log⁡(3sin⁡(nn3+1))log⁡(n)\frac{\log{\left(\frac{3}{\sin{\left(\frac{n}{n^{3} + 1} \right)}} \right)}}{\log{\left(n \right)}} 
log(3/sin(n/(n^3 + 1)))/log(n)
Respuesta numérica [src] 
log(3/sin(n/(n^3 + 1)))/log(n)
log(3/sin(n/(n^3 + 1)))/log(n)
Combinatoria [src] 
            /     1     \
log(3) + log|-----------|
            |   /  n   \|
            |sin|------||
            |   |     3||
            \   \1 + n //
-------------------------
          log(n)
log⁡(1sin⁡(nn3+1))+log⁡(3)log⁡(n)\frac{\log{\left(\frac{1}{\sin{\left(\frac{n}{n^{3} + 1} \right)}} \right)} + \log{\left(3 \right)}}{\log{\left(n \right)}} 
(log(3) + log(1/sin(n/(1 + n^3))))/log(n)
Potencias [src] 
   /        6*I        \
log|-------------------|
   |   -I*n       I*n  |
   |   ------    ------|
   |        3         3|
   |   1 + n     1 + n |
   \- e       + e      /
------------------------
         log(n)
log⁡(6ieinn3+1−e−inn3+1)log⁡(n)\frac{\log{\left(\frac{6 i}{e^{\frac{i n}{n^{3} + 1}} - e^{- \frac{i n}{n^{3} + 1}}} \right)}}{\log{\left(n \right)}} 
log(6*i/(-exp(-i*n/(1 + n^3)) + exp(i*n/(1 + n^3))))/log(n)
Denominador común [src] 
            /     1     \
log(3) + log|-----------|
            |   /  n   \|
            |sin|------||
            |   |     3||
            \   \1 + n //
-------------------------
          log(n)
log⁡(1sin⁡(nn3+1))+log⁡(3)log⁡(n)\frac{\log{\left(\frac{1}{\sin{\left(\frac{n}{n^{3} + 1} \right)}} \right)} + \log{\left(3 \right)}}{\log{\left(n \right)}} 
(log(3) + log(1/sin(n/(1 + n^3))))/log(n)
Parte trigonométrica [src] 
   /     /pi     n   \\
log|3*sec|-- - ------||
   |     |2         3||
   \     \     1 + n //
-----------------------
         log(n)
log⁡(3sec⁡(−nn3+1+π2))log⁡(n)\frac{\log{\left(3 \sec{\left(- \frac{n}{n^{3} + 1} + \frac{\pi}{2} \right)} \right)}}{\log{\left(n \right)}} 
   /     /  n   \\
log|3*csc|------||
   |     |     3||
   \     \1 + n //
------------------
      log(n)
log⁡(3csc⁡(nn3+1))log⁡(n)\frac{\log{\left(3 \csc{\left(\frac{n}{n^{3} + 1} \right)} \right)}}{\log{\left(n \right)}} 
   /        3         \
log|------------------|
   |   /  pi     n   \|
   |cos|- -- + ------||
   |   |  2         3||
   \   \       1 + n //
-----------------------
         log(n)
log⁡(3cos⁡(nn3+1−π2))log⁡(n)\frac{\log{\left(\frac{3}{\cos{\left(\frac{n}{n^{3} + 1} - \frac{\pi}{2} \right)}} \right)}}{\log{\left(n \right)}} 
   /     /  pi     n   \\
log|3*sec|- -- + ------||
   |     |  2         3||
   \     \       1 + n //
-------------------------
          log(n)
log⁡(3sec⁡(nn3+1−π2))log⁡(n)\frac{\log{\left(3 \sec{\left(\frac{n}{n^{3} + 1} - \frac{\pi}{2} \right)} \right)}}{\log{\left(n \right)}} 
   /  /       2/    n     \\\
   |3*|1 + tan |----------|||
   |  |        |  /     3\|||
   |  \        \2*\1 + n ///|
log|------------------------|
   |        /    n     \    |
   |   2*tan|----------|    |
   |        |  /     3\|    |
   \        \2*\1 + n //    /
-----------------------------
            log(n)
log⁡(3(tan⁡2(n2(n3+1))+1)2tan⁡(n2(n3+1)))log⁡(n)\frac{\log{\left(\frac{3 \left(\tan^{2}{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)} + 1\right)}{2 \tan{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)}} \right)}}{\log{\left(n \right)}} 
   /  /       2/    n     \\\
   |3*|1 + cot |----------|||
   |  |        |  /     3\|||
   |  \        \2*\1 + n ///|
log|------------------------|
   |        /    n     \    |
   |   2*cot|----------|    |
   |        |  /     3\|    |
   \        \2*\1 + n //    /
-----------------------------
            log(n)
log⁡(3(cot⁡2(n2(n3+1))+1)2cot⁡(n2(n3+1)))log⁡(n)\frac{\log{\left(\frac{3 \left(\cot^{2}{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)} + 1\right)}{2 \cot{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)}} \right)}}{\log{\left(n \right)}} 
log(3*(1 + cot(n/(2*(1 + n^3)))^2)/(2*cot(n/(2*(1 + n^3)))))/log(n)
Abrimos la expresión [src] 
            /     1     \
         log|-----------|
            |   /  n   \|
            |sin|------||
            |   | 3    ||
log(3)      \   \n  + 1//
------ + ----------------
log(n)        log(n)
log⁡(1sin⁡(nn3+1))log⁡(n)+log⁡(3)log⁡(n)\frac{\log{\left(\frac{1}{\sin{\left(\frac{n}{n^{3} + 1} \right)}} \right)}}{\log{\left(n \right)}} + \frac{\log{\left(3 \right)}}{\log{\left(n \right)}} 
log(3)/log(n) + log(1/sin(n/(n^3 + 1)))/log(n)
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