Sr Examen
¿Cómo vas a descomponer esta ln(1/sin(n/(n^3+1)))/ln(n) expresión en fracciones?
Solución
Ha introducido
[src]
/ 1 \
log|-----------|
| / n \|
|sin|------||
| | 3 ||
\ \n + 1//
----------------
log(n)
$$\frac{\log{\left(\frac{1}{\sin{\left(\frac{n}{n^{3} + 1} \right)}} \right)}}{\log{\left(n \right)}}$$
log(1/sin(n/(n^3 + 1)))/log(n)
Potencias
[src]
/ 2*I \
log|-------------------|
| -I*n I*n |
| ------ ------|
| 3 3|
| 1 + n 1 + n |
\- e + e /
------------------------
log(n)
$$\frac{\log{\left(\frac{2 i}{e^{\frac{i n}{n^{3} + 1}} - e^{- \frac{i n}{n^{3} + 1}}} \right)}}{\log{\left(n \right)}}$$
log(2*i/(-exp(-i*n/(1 + n^3)) + exp(i*n/(1 + n^3))))/log(n)
Parte trigonométrica
[src]
/ 1 \
log|------------------|
| / pi n \|
|cos|- -- + ------||
| | 2 3||
\ \ 1 + n //
-----------------------
log(n)
$$\frac{\log{\left(\frac{1}{\cos{\left(\frac{n}{n^{3} + 1} - \frac{\pi}{2} \right)}} \right)}}{\log{\left(n \right)}}$$
/ /pi n \\
log|sec|-- - ------||
| |2 3||
\ \ 1 + n //
---------------------
log(n)
$$\frac{\log{\left(\sec{\left(- \frac{n}{n^{3} + 1} + \frac{\pi}{2} \right)} \right)}}{\log{\left(n \right)}}$$
/ 2/ n \\
|1 + tan |----------||
| | / 3\||
| \2*\1 + n //|
log|--------------------|
| / n \ |
| 2*tan|----------| |
| | / 3\| |
\ \2*\1 + n // /
-------------------------
log(n)
$$\frac{\log{\left(\frac{\tan^{2}{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)} + 1}{2 \tan{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)}} \right)}}{\log{\left(n \right)}}$$
/ 2/ n \\
|1 + cot |----------||
| | / 3\||
| \2*\1 + n //|
log|--------------------|
| / n \ |
| 2*cot|----------| |
| | / 3\| |
\ \2*\1 + n // /
-------------------------
log(n)
$$\frac{\log{\left(\frac{\cot^{2}{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)} + 1}{2 \cot{\left(\frac{n}{2 \left(n^{3} + 1\right)} \right)}} \right)}}{\log{\left(n \right)}}$$
/ / pi n \\
log|sec|- -- + ------||
| | 2 3||
\ \ 1 + n //
-----------------------
log(n)
$$\frac{\log{\left(\sec{\left(\frac{n}{n^{3} + 1} - \frac{\pi}{2} \right)} \right)}}{\log{\left(n \right)}}$$
/ / n \\
log|csc|------||
| | 3||
\ \1 + n //
----------------
log(n)
$$\frac{\log{\left(\csc{\left(\frac{n}{n^{3} + 1} \right)} \right)}}{\log{\left(n \right)}}$$
log(csc(n/(1 + n^3)))/log(n)