Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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- Derivada de:
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Derivada de -5*tan(2*t)-4*cot(4*t)
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Derivada de (3x+6)^2
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Derivada de 3^(x*x)
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Derivada de 2*x-8/x
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Expresiones idénticas
- (x/(ln(uno +x^ dos)/(uno +x^ dos)))*arсctg(x/(ln(uno +x^ dos)/(uno +x^ dos)))
- (x dividir por (ln(1 más x al cuadrado ) dividir por (1 más x al cuadrado ))) multiplicar por arсctg(x dividir por (ln(1 más x al cuadrado ) dividir por (1 más x al cuadrado )))
- (x dividir por (ln(uno más x en el grado dos) dividir por (uno más x en el grado dos))) multiplicar por arсctg(x dividir por (ln(uno más x en el grado dos) dividir por (uno más x en el grado dos)))
- (x/(ln(1+x2)/(1+x2)))*arсctg(x/(ln(1+x2)/(1+x2)))
- x/ln1+x2/1+x2*arсctgx/ln1+x2/1+x2
- (x/(ln(1+x²)/(1+x²)))*arсctg(x/(ln(1+x²)/(1+x²)))
- (x/(ln(1+x en el grado 2)/(1+x en el grado 2)))*arсctg(x/(ln(1+x en el grado 2)/(1+x en el grado 2)))
- (x/(ln(1+x^2)/(1+x^2)))arсctg(x/(ln(1+x^2)/(1+x^2)))
- (x/(ln(1+x2)/(1+x2)))arсctg(x/(ln(1+x2)/(1+x2)))
- x/ln1+x2/1+x2arсctgx/ln1+x2/1+x2
- x/ln1+x^2/1+x^2arсctgx/ln1+x^2/1+x^2
- (x dividir por (ln(1+x^2) dividir por (1+x^2)))*arсctg(x dividir por (ln(1+x^2) dividir por (1+x^2)))
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Expresiones semejantes
- (x/(ln(1-x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))
- (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1-x^2)/(1+x^2)))
- (x/(ln(1+x^2)/(1-x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))
- (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1-x^2)))
Derivada de (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))
Solución
Primera derivada
[src]
/ 2 / / 2\\\
| / 2\ | 2*x 2*x*log\1 + x /||
| x*\1 + x / *|- --------- + ---------------||
| | 2 2 ||
2 | | / 2\ / 2\ ||
1 + x | 1 \ \1 + x / \1 + x / /|
/ 2 / / 2\\\ x*-----------*|------------- + -------------------------------------------|
| / 2\ | 2*x 2*x*log\1 + x /|| / 2\ |/ / 2\\ 2/ 2\ |
| x*\1 + x / *|- --------- + ---------------|| log\1 + x / ||log\1 + x /| log \1 + x / |
| | 2 2 || ||-----------| |
| | / 2\ / 2\ || || 2 | |
| 1 \ \1 + x / \1 + x / /| / x \ \\ 1 + x / /
|------------- + -------------------------------------------|*acot|-------------| - ---------------------------------------------------------------------------
|/ / 2\\ 2/ 2\ | |/ / 2\\| 2
||log\1 + x /| log \1 + x / | ||log\1 + x /|| 2 / 2\
||-----------| | ||-----------|| x *\1 + x /
|| 2 | | || 2 || 1 + ------------
\\ 1 + x / / \\ 1 + x // 2/ 2\
log \1 + x /
$$- \frac{x \frac{x^{2} + 1}{\log{\left(x^{2} + 1 \right)}} \left(\frac{x \left(x^{2} + 1\right)^{2} \left(\frac{2 x \log{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 x}{\left(x^{2} + 1\right)^{2}}\right)}{\log{\left(x^{2} + 1 \right)}^{2}} + \frac{1}{\frac{1}{x^{2} + 1} \log{\left(x^{2} + 1 \right)}}\right)}{\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1} + \left(\frac{x \left(x^{2} + 1\right)^{2} \left(\frac{2 x \log{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 x}{\left(x^{2} + 1\right)^{2}}\right)}{\log{\left(x^{2} + 1 \right)}^{2}} + \frac{1}{\frac{1}{x^{2} + 1} \log{\left(x^{2} + 1 \right)}}\right) \operatorname{acot}{\left(\frac{x}{\frac{1}{x^{2} + 1} \log{\left(x^{2} + 1 \right)}} \right)}$$
Segunda derivada
[src]
/ / / 2 / / 2\\\ / 2 \\\
| | / 2\ | 2 2*x *\-1 + log\1 + x //| | 2 2*x |||
| | \1 + x /*|1 + x + -----------------------|*|1 + 3*x - -----------|||
| | 2 2 / / 2\\ 2 / 2\ 2 / / 2\\ | / 2\ | | / 2\|||
| 2 / 2\ | / 2\ 6*x 4*x *\-1 + log\1 + x // 4*x *log\1 + x / 4*x *\-1 + log\1 + x // \ log\1 + x / / \ log\1 + x //||
| x *\1 + x /*|3 - 3*log\1 + x / - ------ - ----------------------- + ---------------- + ----------------------- + --------------------------------------------------------------------||
| 2 | 2 2 2 / 2\ / 2\ / 2\ ||
| / 2 / / 2\\\ | 1 + x 1 + x 1 + x \1 + x /*log\1 + x / | 2 / 2\ | ||
| | 2 2*x *\-1 + log\1 + x //| / 2 / 1 \ / / 2\\\ | | x *\1 + x / | / 2\ ||
| |1 + x + -----------------------| | 2*x *|1 - -----------|*\-1 + log\1 + x //| | |1 + ------------|*log\1 + x / ||
| | / 2\ | | 2 2 / 2\ 2 / / 2\\ 2 / / 2\\ | / 2\| | / / 2\\ | | 2/ 2\| ||
| \ log\1 + x / / | / 2\ 6*x 4*x *log\1 + x / 2*x *\-1 + log\1 + x // 2*x *\-1 + log\1 + x // \ log\1 + x // | | x*\1 + x /| \ \ log \1 + x // /|
2*|- ----------------------------------- + x*|-3 + 3*log\1 + x / + ------ - ---------------- + ----------------------- - ----------------------- + -----------------------------------------|*acot|-----------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 2 | 2 2 2 / 2\ / 2\ 2 | | / 2\| / 2\ |
| 2 / 2\ \ 1 + x 1 + x 1 + x \1 + x /*log\1 + x / 1 + x / \log\1 + x // | 2 / 2\ | |
| x *\1 + x / | x *\1 + x / | / 2\ |
| 1 + ------------ |1 + ------------|*log\1 + x / |
| 2/ 2\ | 2/ 2\| |
\ log \1 + x / \ log \1 + x // /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2/ 2\
log \1 + x /
$$\frac{2 \left(\frac{x^{2} \left(x^{2} + 1\right) \left(- \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} + \frac{\left(x^{2} + 1\right) \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right) \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} - 3 \log{\left(x^{2} + 1 \right)} + 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} + x \left(\frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{6 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right) \operatorname{acot}{\left(\frac{x \left(x^{2} + 1\right)}{\log{\left(x^{2} + 1 \right)}} \right)} - \frac{\left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)^{2}}{\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1}\right)}{\log{\left(x^{2} + 1 \right)}^{2}}$$
Tercera derivada
[src]
/ / 2 \ \
| | / 2 2 / 2\\ / 2 2 / 2\\ / 2 / / 2\\\ / 2 4 4 2 / 2\\ / 2 2 / 2\\ / 2 \ / 2 2 / 2\ 2 / / 2\\ 2 / / 2\\\ 2 / 2 \ / 2 / / 2\\\| |
| | 2 | / 2\ 6*x 4*x *log\1 + x /| 2 | / 2\ 22*x 12*x *log\1 + x /| | 2 2*x *\-1 + log\1 + x //| |/ 2\ 4 12*x 2 / 2\ 12*x 10*x *\1 + x /| 2 / 1 \ / / 2\\ 2 | / 2\ 6*x 4*x *log\1 + x /| 2 / 2\ | 2 2*x | | / 2\ 6*x 4*x *log\1 + x / 4*x *\-1 + log\1 + x // 4*x *\-1 + log\1 + x //| 2 / 2\ | 2 2*x | | 2 2*x *\-1 + log\1 + x //|| / / 2 / / 2\\\ / 2 \\|
| | 8*x *|1 - log\1 + x / - ------ + ----------------| 2*x *|9 - 6*log\1 + x / - ------ + -----------------| |1 + x + -----------------------|*|\1 + x / + 4*x - ----------- + 10*x *\1 + x / + ------------ - --------------| 2*x *|1 - -----------|*\-1 + log\1 + x // 8*x *|1 - log\1 + x / - ------ + ----------------| 4*x *\1 + x /*|1 + 3*x - -----------|*|-3 + 3*log\1 + x / + ------ - ---------------- + ----------------------- - -----------------------| 4*x *\1 + x / *|1 + 3*x - -----------| *|1 + x + -----------------------|| | / 2\ | 2 2*x *\-1 + log\1 + x //| | 2 2*x |||
| | 2 2 / 2\ | 2 2 | | 2 2 | 4 / / 2\\ 2 / / 2\\ | / 2\ | | / 2\ 2/ 2\ / 2\ | 4 / / 2\\ 2 / / 2\\ | / 2\| | 2 2 | 4 / / 2\\ | / 2\| | 2 2 2 / 2\ / 2\ | | / 2\| | / 2\ || | \1 + x /*|1 + x + -----------------------|*|1 + 3*x - -----------|||
| / 2\ | / 2\ 18*x 12*x *log\1 + x / \ 1 + x 1 + x / \ 1 + x 1 + x / 8*x *\-1 + log\1 + x // 14*x *\-1 + log\1 + x // \ log\1 + x / / \ log\1 + x / log \1 + x / log\1 + x / / 24*x *\-1 + log\1 + x // 14*x *\-1 + log\1 + x // \ log\1 + x // \ 1 + x 1 + x / 24*x *\-1 + log\1 + x // \ log\1 + x // \ 1 + x 1 + x 1 + x \1 + x /*log\1 + x / / \ log\1 + x // \ log\1 + x / /| / 2 / / 2\\\ | 2 2 / / 2\\ 2 / 2\ 2 / / 2\\ | / 2\ | | / 2\|||
|/ / / 2 2 / 2\\ \ \ x*\1 + x /*|-3 + 3*log\1 + x / + ------ - ----------------- - -------------------------------------------------- + ----------------------------------------------------- + ----------------------- + ------------------------ - -------------------------------------------------------------------------------------------------------------------- - ------------------------ - ------------------------ + ----------------------------------------- + -------------------------------------------------- + ------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------| | 2 2*x *\-1 + log\1 + x //| | / 2\ 6*x 4*x *\-1 + log\1 + x // 4*x *log\1 + x / 4*x *\-1 + log\1 + x // \ log\1 + x / / \ log\1 + x //||
|| | | / 2\ 6*x 4*x *log\1 + x /| 2 / 1 \ / / 2\\ 2 / 1 \ / / 2\\| | | 2 2 2 2 2 2 / 2\ 2 / 2\ / 2\ 2 / 2\ / 2\ 2 / 2\ 2 | / 2 / 1 \ / / 2\\\ 3*x*|1 + x + -----------------------|*|3 - 3*log\1 + x / - ------ - ----------------------- + ---------------- + ----------------------- + --------------------------------------------------------------------||
|| | 3*|1 - log\1 + x / - ------ + ----------------| 2*x *|1 - -----------|*\-1 + log\1 + x // 2*x *|1 - -----------|*\-1 + log\1 + x //| | | 1 + x 1 + x 1 + x 1 + x / 2\ 1 + x | 2 / 2\ | / 2\ / 2\ \1 + x /*log\1 + x / 1 + x \1 + x /*log\1 + x / / 2\ 2/ 2\ | 2 / 2\ | / 2\ | | 2*x *|1 - -----------|*\-1 + log\1 + x //| | / 2\ | | 2 2 2 / 2\ / 2\ / 2\ ||
|| | / 2\ / 2 2 / 2\\ / 2 2 \ | 2 2 | 2 2 / / 2\\ 2 / / 2\\ | / 2\| 2 / / 2\\ | / 2\| | | | \1 + x / | x *\1 + x / | / 2\ \1 + x / *log\1 + x / \1 + x / *log \1 + x / | x *\1 + x / | 2/ 2\ | 2 / 2\ | | / 2 / / 2\\\ | 2 2 / 2\ 2 / / 2\\ 2 / / 2\\ | / 2\| | \ log\1 + x / / | 1 + x 1 + x 1 + x \1 + x /*log\1 + x / | 2 / 2\ | ||
|| 2 | / 2\ -1 + log\1 + x / / 1 \ | / 2\ 6*x 4*x *log\1 + x /| / / 2\\ | 1 4*x 2*x | \ 1 + x 1 + x / 4*x 2*x *\-1 + log\1 + x // 6*x *\-1 + log\1 + x // \ log\1 + x // 6*x *\-1 + log\1 + x // \ log\1 + x // | 2 / 1 \ / / 2\\| | |1 + ------------|*log\1 + x / |1 + ------------|*log \1 + x / | x *\1 + x / | 3/ 2\ | | 2 2*x *\-1 + log\1 + x //| | / 2\ 6*x 4*x *log\1 + x / 2*x *\-1 + log\1 + x // 2*x *\-1 + log\1 + x // \ log\1 + x // | | | x *\1 + x / | / 2\ ||
|| 2*x *|-5 + 2*log\1 + x / + ---------------- + |1 - -----------|*|1 - log\1 + x / - ------ + ----------------| + \-1 + log\1 + x //*|-1 + ----------- - --------------------- + --------------------| - ----------------------------------------------- + ------ - ----------------------- - ----------------------- - ----------------------------------------- + ----------------------- + -----------------------------------------| 6*x *|1 - -----------|*\-1 + log\1 + x //| | | 2/ 2\| | 2/ 2\| |1 + ------------| *log \1 + x / | 3*x*|1 + x + -----------------------|*|-3 + 3*log\1 + x / + ------ - ---------------- + ----------------------- - ----------------------- + -----------------------------------------| | |1 + ------------|*log\1 + x / ||
|| 2 2 / 2\ | / 2\ | / 2\| | 2 2 | | / 2\ / 2\ 2/ 2\ / 2\ / 2\| / 2\ 2 2 / 2\ 2/ 2\ 2 / 2\ / 2\ / 2\ / 2\ | 2 / / 2\\ 2 / / 2\\ | / 2\| | / / 2\\ | \ log \1 + x // \ log \1 + x // | 2/ 2\| | | / 2\ | | 2 2 2 / 2\ / 2\ 2 | | | 2/ 2\| ||
|| / 2\ 18*x 12*x *log\1 + x / \ log\1 + x / \ log\1 + x // \ 1 + x 1 + x / \ log\1 + x / \1 + x /*log \1 + x / \1 + x /*log\1 + x // log\1 + x / 1 + x 1 + x \1 + x /*log \1 + x / 1 + x \1 + x /*log\1 + x / \1 + x /*log\1 + x / / 6*x *\-1 + log\1 + x // 6*x *\-1 + log\1 + x // \ log\1 + x // | | x*\1 + x /| \ \ log \1 + x // / \ log\1 + x / / \ 1 + x 1 + x 1 + x \1 + x /*log\1 + x / 1 + x / \ \ log \1 + x // /|
2*||-3 + 3*log\1 + x / + ------ - ----------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- - ----------------------- + -----------------------------------------|*acot|-----------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|| 2 2 2 2 / 2\ / 2\ 2 | | / 2\| / 2\ / 2\ / 2\ |
|\ 1 + x 1 + x 1 + x 1 + x \1 + x /*log\1 + x / 1 + x / \log\1 + x // | 2 / 2\ | | 2 / 2\ | | 2 / 2\ | |
| | x *\1 + x / | / 2\ | x *\1 + x / | / 2\ | x *\1 + x / | / 2\ |
| |1 + ------------|*log\1 + x / |1 + ------------|*log\1 + x / |1 + ------------|*log\1 + x / |
| | 2/ 2\| | 2/ 2\| | 2/ 2\| |
\ \ log \1 + x // \ log \1 + x // \ log \1 + x // /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2/ 2\
log \1 + x /
$$\frac{2 \left(- \frac{x \left(x^{2} + 1\right) \left(\frac{8 x^{4} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{24 x^{4} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right)^{2} \log{\left(x^{2} + 1 \right)}} + \frac{24 x^{4} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right)^{2} \log{\left(x^{2} + 1 \right)}^{2}} + \frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{4 x^{2} \left(x^{2} + 1\right)^{2} \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right)^{2} \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right)^{2} \log{\left(x^{2} + 1 \right)}^{3}} - \frac{4 x^{2} \left(x^{2} + 1\right) \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right) \left(\frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{6 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}^{2}} + \frac{14 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{14 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{8 x^{2} \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right)}{x^{2} + 1} + \frac{8 x^{2} \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{2 x^{2} \left(\frac{12 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{22 x^{2}}{x^{2} + 1} - 6 \log{\left(x^{2} + 1 \right)} + 9\right)}{x^{2} + 1} - \frac{12 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{18 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3 - \frac{\left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right) \left(4 x^{4} - \frac{12 x^{4}}{\log{\left(x^{2} + 1 \right)}} + \frac{12 x^{4}}{\log{\left(x^{2} + 1 \right)}^{2}} + 10 x^{2} \left(x^{2} + 1\right) - \frac{10 x^{2} \left(x^{2} + 1\right)}{\log{\left(x^{2} + 1 \right)}} + \left(x^{2} + 1\right)^{2}\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}}\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{3 x \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right) \left(- \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} + \frac{\left(x^{2} + 1\right) \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right) \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} - 3 \log{\left(x^{2} + 1 \right)} + 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{3 x \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right) \left(\frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{6 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} + \left(\frac{6 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{2 x^{2} \left(- \frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}^{2}} + \frac{4 x^{2}}{x^{2} + 1} + \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right) + \left(\log{\left(x^{2} + 1 \right)} - 1\right) \left(\frac{2 x^{2}}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2}}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}^{2}} - 1 + \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) + \frac{\log{\left(x^{2} + 1 \right)} - 1}{\log{\left(x^{2} + 1 \right)}} - \frac{3 \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right)}{\log{\left(x^{2} + 1 \right)}} + 2 \log{\left(x^{2} + 1 \right)} - 5\right)}{x^{2} + 1} - \frac{12 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{18 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right) \operatorname{acot}{\left(\frac{x \left(x^{2} + 1\right)}{\log{\left(x^{2} + 1 \right)}} \right)}\right)}{\log{\left(x^{2} + 1 \right)}^{2}}$$
Gráfico