Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t)))
¿Cómo vas a descomponer esta tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t))) expresión en fracciones?
Solución
Ha introducido
[src]
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|/ / 2 \ \ / 2 \ / 2 \|
atan(t) ||log(tan(t)) \1 + tan (t)/*atan(t)| / 2 \ \1 + tan (t)/ *atan(t) 2*t*log(tan(t)) 2*\1 + tan (t)/|
tan (t)*||----------- + ---------------------| + 2*\1 + tan (t)/*atan(t) - ---------------------- - --------------- + ---------------|
|| 2 tan(t) | 2 2 / 2\ |
|\ 1 + t / tan (t) / 2\ \1 + t /*tan(t)|
\ \1 + t / /
$$\left(\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(- \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(\left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} + 2 \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}\right)\right)\right) + \frac{2 \left(\tan^{2}{\left(t \right)} + 1\right)}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}$$
tan(t)^atan(t)*((log(tan(t))/(1 + t^2) + ((1 + tan(t)^2)*atan(t))/tan(t))^2 + (2*(1 + tan(t)^2))*atan(t) - (1 + tan(t)^2)^2*atan(t)/tan(t)^2 - (2*t)*log(tan(t))/(1 + t^2)^2 + (2*(1 + tan(t)^2))/(((1 + t^2)*tan(t))))
Simplificación general
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/ 2 2 2 \
|/ / 2\ \ / 2\ / 2\ / 2\ 2 |
-2 + atan(t) || \1 + t /*atan(t)| \2 + 2*t /*tan(t) \1 + t / *atan(t) 2 2*\1 + t / *tan (t)*atan(t)|
tan (t)*||log(tan(t))*tan(t) + ----------------| + ----------------- - ----------------- - 2*t*tan (t)*log(tan(t)) + ---------------------------|
|| 2 | 2 4 2 |
\\ cos (t) / cos (t) cos (t) cos (t) /
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2
/ 2\
\1 + t /
$$\frac{\left(- 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} + \frac{2 \left(t^{2} + 1\right)^{2} \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{\cos^{2}{\left(t \right)}} - \frac{\left(t^{2} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\cos^{4}{\left(t \right)}} + \frac{\left(2 t^{2} + 2\right) \tan{\left(t \right)}}{\cos^{2}{\left(t \right)}} + \left(\frac{\left(t^{2} + 1\right) \operatorname{atan}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)}\right)^{2}\right) \tan^{\operatorname{atan}{\left(t \right)} - 2}{\left(t \right)}}{\left(t^{2} + 1\right)^{2}}$$
tan(t)^(-2 + atan(t))*((log(tan(t))*tan(t) + (1 + t^2)*atan(t)/cos(t)^2)^2 + (2 + 2*t^2)*tan(t)/cos(t)^2 - (1 + t^2)^2*atan(t)/cos(t)^4 - 2*t*tan(t)^2*log(tan(t)) + 2*(1 + t^2)^2*tan(t)^2*atan(t)/cos(t)^2)/(1 + t^2)^2
Denominador racional
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/ 4 / 2 / / 2 2 \ 2 2 \ 2 \ \
atan(t) |/ 2\ 4 / 2 \ / 2\ |/ 2\ | 2 |/ / 2\ / 2 \ \ / 2\ 2 / 2 \ | / 2\ / 2 \ 2 | / 2\ 4 | |
tan (t)*\\1 + t / *tan (t)*\2 + 2*tan (t)/ + \1 + t /*\\1 + t / *\tan (t)*\\log(tan(t))*tan(t) + \1 + t /*\1 + tan (t)/*atan(t)/ + \1 + t / *tan (t)*\2 + 2*tan (t)/*atan(t)/ - \1 + t / *\1 + tan (t)/ *tan (t)*atan(t)/ - 2*t*\1 + t / *tan (t)*log(tan(t))/*tan(t)/
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5
/ 2\ 5
\1 + t / *tan (t)
$$\frac{\left(\left(t^{2} + 1\right)^{4} \left(2 \tan^{2}{\left(t \right)} + 2\right) \tan^{4}{\left(t \right)} + \left(t^{2} + 1\right) \left(- 2 t \left(t^{2} + 1\right)^{2} \log{\left(\tan{\left(t \right)} \right)} \tan^{4}{\left(t \right)} + \left(t^{2} + 1\right)^{2} \left(- \left(t^{2} + 1\right)^{2} \left(\tan^{2}{\left(t \right)} + 1\right)^{2} \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)} + \left(\left(t^{2} + 1\right)^{2} \left(2 \tan^{2}{\left(t \right)} + 2\right) \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)} + \left(\left(t^{2} + 1\right) \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)}\right)^{2}\right) \tan^{2}{\left(t \right)}\right)\right) \tan{\left(t \right)}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{\left(t^{2} + 1\right)^{5} \tan^{5}{\left(t \right)}}$$
tan(t)^atan(t)*((1 + t^2)^4*tan(t)^4*(2 + 2*tan(t)^2) + (1 + t^2)*((1 + t^2)^2*(tan(t)^2*((log(tan(t))*tan(t) + (1 + t^2)*(1 + tan(t)^2)*atan(t))^2 + (1 + t^2)^2*tan(t)^2*(2 + 2*tan(t)^2)*atan(t)) - (1 + t^2)^2*(1 + tan(t)^2)^2*tan(t)^2*atan(t)) - 2*t*(1 + t^2)^2*tan(t)^4*log(tan(t)))*tan(t))/((1 + t^2)^5*tan(t)^5)
Potencias
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atan(t) ||log(tan(t)) \1 + tan (t)/*atan(t)| / 2 \ 2 + 2*tan (t) \1 + tan (t)/ *atan(t) 2*t*log(tan(t))|
tan (t)*||----------- + ---------------------| + \2 + 2*tan (t)/*atan(t) + --------------- - ---------------------- - ---------------|
|| 2 tan(t) | / 2\ 2 2 |
|\ 1 + t / \1 + t /*tan(t) tan (t) / 2\ |
\ \1 + t / /
$$\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} - \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(2 \tan^{2}{\left(t \right)} + 2\right) \operatorname{atan}{\left(t \right)} + \frac{2 \tan^{2}{\left(t \right)} + 2}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}$$
/ 2 2 \
|/ / 2\ \ / 2\ / 2\ |
|| | / I*t -I*t\ | | | / I*t -I*t\ | 2 | / I*t -I*t\ | |
|| / / I*t -I*t\\ | \- e + e / | / I*t -I*t\ | / / I*t -I*t\\ | \- e + e / | / I*t -I*t\ | 2*\- e + e / | / I*t -I*t\|
|| |I*\- e + e /| I*|1 - -----------------|*\e + e /*atan(t)| |I*\- e + e /| |1 - -----------------| *\e + e / *atan(t) I*|2 - -------------------|*\e + e /|
atan(t) ||log|------------------| | 2 | | / 2\ 2*t*log|------------------| | 2 | | 2 | |
/ / I*t -I*t\\ || | I*t -I*t | | / I*t -I*t\ | | | / I*t -I*t\ | | I*t -I*t | | / I*t -I*t\ | | / I*t -I*t\ | |
|I*\- e + e /| || \ e + e / \ \e + e / / | | 2*\- e + e / | \ e + e / \ \e + e / / \ \e + e / / |
|------------------| *||----------------------- - ------------------------------------------------| + |2 - -------------------|*atan(t) - --------------------------- + ------------------------------------------------ - ------------------------------------------|
| I*t -I*t | || 2 I*t -I*t | | 2 | 2 2 / 2\ / I*t -I*t\ |
\ e + e / |\ 1 + t - e + e / | / I*t -I*t\ | / 2\ / I*t -I*t\ \1 + t /*\- e + e / |
\ \ \e + e / / \1 + t / \- e + e / /
$$\left(\frac{i \left(- e^{i t} + e^{- i t}\right)}{e^{i t} + e^{- i t}}\right)^{\operatorname{atan}{\left(t \right)}} \left(- \frac{2 t \log{\left(\frac{i \left(- e^{i t} + e^{- i t}\right)}{e^{i t} + e^{- i t}} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(- \frac{2 \left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 2\right) \operatorname{atan}{\left(t \right)} + \frac{\left(- \frac{\left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 1\right)^{2} \left(e^{i t} + e^{- i t}\right)^{2} \operatorname{atan}{\left(t \right)}}{\left(- e^{i t} + e^{- i t}\right)^{2}} + \left(- \frac{i \left(- \frac{\left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 1\right) \left(e^{i t} + e^{- i t}\right) \operatorname{atan}{\left(t \right)}}{- e^{i t} + e^{- i t}} + \frac{\log{\left(\frac{i \left(- e^{i t} + e^{- i t}\right)}{e^{i t} + e^{- i t}} \right)}}{t^{2} + 1}\right)^{2} - \frac{i \left(- \frac{2 \left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 2\right) \left(e^{i t} + e^{- i t}\right)}{\left(t^{2} + 1\right) \left(- e^{i t} + e^{- i t}\right)}\right)$$
(i*(-exp(i*t) + exp(-i*t))/(exp(i*t) + exp(-i*t)))^atan(t)*((log(i*(-exp(i*t) + exp(-i*t))/(exp(i*t) + exp(-i*t)))/(1 + t^2) - i*(1 - (-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*(exp(i*t) + exp(-i*t))*atan(t)/(-exp(i*t) + exp(-i*t)))^2 + (2 - 2*(-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*atan(t) - 2*t*log(i*(-exp(i*t) + exp(-i*t))/(exp(i*t) + exp(-i*t)))/(1 + t^2)^2 + (1 - (-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)^2*(exp(i*t) + exp(-i*t))^2*atan(t)/(-exp(i*t) + exp(-i*t))^2 - i*(2 - 2*(-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*(exp(i*t) + exp(-i*t))/((1 + t^2)*(-exp(i*t) + exp(-i*t))))
Unión de expresiones racionales
[src]
/ 2 2 2 2 \
atan(t) |/ / 2\ / 2 \ \ / 2\ / 2 \ 2 / 2\ / 2 \ / 2\ 2 / 2 \ |
tan (t)*\\log(tan(t))*tan(t) + \1 + t /*\1 + tan (t)/*atan(t)/ - \1 + t / *\1 + tan (t)/ *atan(t) - 2*t*tan (t)*log(tan(t)) + 2*\1 + t /*\1 + tan (t)/*tan(t) + 2*\1 + t / *tan (t)*\1 + tan (t)/*atan(t)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\ 2
\1 + t / *tan (t)
$$\frac{\left(- 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} - \left(t^{2} + 1\right)^{2} \left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)} + 2 \left(t^{2} + 1\right)^{2} \left(\tan^{2}{\left(t \right)} + 1\right) \tan^{2}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \left(t^{2} + 1\right) \left(\tan^{2}{\left(t \right)} + 1\right) \tan{\left(t \right)} + \left(\left(t^{2} + 1\right) \left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)}\right)^{2}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{\left(t^{2} + 1\right)^{2} \tan^{2}{\left(t \right)}}$$
tan(t)^atan(t)*((log(tan(t))*tan(t) + (1 + t^2)*(1 + tan(t)^2)*atan(t))^2 - (1 + t^2)^2*(1 + tan(t)^2)^2*atan(t) - 2*t*tan(t)^2*log(tan(t)) + 2*(1 + t^2)*(1 + tan(t)^2)*tan(t) + 2*(1 + t^2)^2*tan(t)^2*(1 + tan(t)^2)*atan(t))/((1 + t^2)^2*tan(t)^2)
Denominador común
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2 atan(t) atan(t) 3 atan(t) atan(t) 4 2 atan(t) 2 2 atan(t) 4 atan(t) 2 atan(t) 2 2 atan(t) 2 3 atan(t) 2 atan(t) 2 atan(t) 3 atan(t) atan(t) 2 3 atan(t) 2 atan(t)
atan (t)*tan (t) - tan (t)*atan(t) + 2*tan (t)*tan (t) + 2*tan (t)*tan(t) + t *atan (t)*tan (t) + log (tan(t))*tan (t)*tan (t) - t *tan (t)*atan(t) - 2*t *tan (t)*atan(t) + 2*t *atan (t)*tan (t) + 2*t *tan (t)*tan (t) + 2*t *tan (t)*tan(t) - 2*t*tan (t)*tan (t)*log(tan(t)) + 2*tan (t)*tan (t)*atan(t)*log(tan(t)) + 2*tan (t)*atan(t)*log(tan(t))*tan(t) + 2*t *tan (t)*tan (t)*atan(t)*log(tan(t)) + 2*t *tan (t)*atan(t)*log(tan(t))*tan(t) 2 atan(t) 2 2 atan(t) 2 atan(t)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*atan (t)*tan (t) + atan (t)*tan (t)*tan (t) + tan (t)*tan (t)*atan(t)
2 4 2 2 2
tan (t) + t *tan (t) + 2*t *tan (t)
$$\tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \frac{t^{4} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} - t^{4} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 t^{2} \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 t^{2} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} - 2 t^{2} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} - 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)}^{2} \tan^{2}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{3}{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + 2 \tan{\left(t \right)} \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} + \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} - \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)} \operatorname{atan}{\left(t \right)}}{t^{4} \tan^{2}{\left(t \right)} + 2 t^{2} \tan^{2}{\left(t \right)} + \tan^{2}{\left(t \right)}}$$
(atan(t)^2*tan(t)^atan(t) - tan(t)^atan(t)*atan(t) + 2*tan(t)^3*tan(t)^atan(t) + 2*tan(t)^atan(t)*tan(t) + t^4*atan(t)^2*tan(t)^atan(t) + log(tan(t))^2*tan(t)^2*tan(t)^atan(t) - t^4*tan(t)^atan(t)*atan(t) - 2*t^2*tan(t)^atan(t)*atan(t) + 2*t^2*atan(t)^2*tan(t)^atan(t) + 2*t^2*tan(t)^3*tan(t)^atan(t) + 2*t^2*tan(t)^atan(t)*tan(t) - 2*t*tan(t)^2*tan(t)^atan(t)*log(tan(t)) + 2*tan(t)^3*tan(t)^atan(t)*atan(t)*log(tan(t)) + 2*tan(t)^atan(t)*atan(t)*log(tan(t))*tan(t) + 2*t^2*tan(t)^3*tan(t)^atan(t)*atan(t)*log(tan(t)) + 2*t^2*tan(t)^atan(t)*atan(t)*log(tan(t))*tan(t))/(tan(t)^2 + t^4*tan(t)^2 + 2*t^2*tan(t)^2) + 2*atan(t)^2*tan(t)^atan(t) + atan(t)^2*tan(t)^2*tan(t)^atan(t) + tan(t)^2*tan(t)^atan(t)*atan(t)
Compilar la expresión
[src]
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|/ / 2 \ \ 2 / 2 \ |
atan(t) ||log(tan(t)) \1 + tan (t)/*atan(t)| / 2 \ 2 + 2*tan (t) \1 + tan (t)/ *atan(t) 2*t*log(tan(t))|
tan (t)*||----------- + ---------------------| + \2 + 2*tan (t)/*atan(t) + --------------- - ---------------------- - ---------------|
|| 2 tan(t) | / 2\ 2 2 |
|\ 1 + t / \1 + t /*tan(t) tan (t) / 2\ |
\ \1 + t / /
$$\left(- \frac{2 t \log{\left(\tan{\left(t \right)} \right)}}{\left(t^{2} + 1\right)^{2}} + \left(\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \operatorname{atan}{\left(t \right)}}{\tan{\left(t \right)}} + \frac{\log{\left(\tan{\left(t \right)} \right)}}{t^{2} + 1}\right)^{2} - \frac{\left(\tan^{2}{\left(t \right)} + 1\right)^{2} \operatorname{atan}{\left(t \right)}}{\tan^{2}{\left(t \right)}} + \left(2 \tan^{2}{\left(t \right)} + 2\right) \operatorname{atan}{\left(t \right)} + \frac{2 \tan^{2}{\left(t \right)} + 2}{\left(t^{2} + 1\right) \tan{\left(t \right)}}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}$$
tan(t)^atan(t)*((log(tan(t))/(1 + t^2) + (1 + tan(t)^2)*atan(t)/tan(t))^2 + (2 + 2*tan(t)^2)*atan(t) + (2 + 2*tan(t)^2)/((1 + t^2)*tan(t)) - (1 + tan(t)^2)^2*atan(t)/tan(t)^2 - 2*t*log(tan(t))/(1 + t^2)^2)
Combinatoria
[src]
atan(t) / 2 3 4 2 2 4 2 2 4 4 2 2 2 2 3 2 2 2 4 2 4 4 4 2 2 2 4 2 4 4 2 2 3 2 2 2 2 3 2 \
tan (t)*\atan (t) - atan(t) + 2*tan (t) + 2*tan(t) + t *atan (t) + atan (t)*tan (t) + log (tan(t))*tan (t) + tan (t)*atan(t) - t *atan(t) - 2*t *atan(t) + 2*t *atan (t) + 2*t *tan (t) + 2*t *tan(t) + 2*atan (t)*tan (t) + t *atan (t)*tan (t) + t *tan (t)*atan(t) - 2*t*tan (t)*log(tan(t)) + 2*t *atan (t)*tan (t) + 2*t *tan (t)*atan(t) + 2*t *atan (t)*tan (t) + 2*tan (t)*atan(t)*log(tan(t)) + 2*atan(t)*log(tan(t))*tan(t) + 4*t *atan (t)*tan (t) + 2*t *tan (t)*atan(t)*log(tan(t)) + 2*t *atan(t)*log(tan(t))*tan(t)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\ 2
\1 + t / *tan (t)
$$\frac{\left(t^{4} \tan^{4}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + t^{4} \tan^{4}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{4} \tan^{2}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + t^{4} \operatorname{atan}^{2}{\left(t \right)} - t^{4} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \tan^{4}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + 2 t^{2} \tan^{4}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 t^{2} \tan^{3}{\left(t \right)} + 4 t^{2} \tan^{2}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + 2 t^{2} \tan{\left(t \right)} + 2 t^{2} \operatorname{atan}^{2}{\left(t \right)} - 2 t^{2} \operatorname{atan}{\left(t \right)} - 2 t \log{\left(\tan{\left(t \right)} \right)} \tan^{2}{\left(t \right)} + \log{\left(\tan{\left(t \right)} \right)}^{2} \tan^{2}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan^{3}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \log{\left(\tan{\left(t \right)} \right)} \tan{\left(t \right)} \operatorname{atan}{\left(t \right)} + \tan^{4}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + \tan^{4}{\left(t \right)} \operatorname{atan}{\left(t \right)} + 2 \tan^{3}{\left(t \right)} + 2 \tan^{2}{\left(t \right)} \operatorname{atan}^{2}{\left(t \right)} + 2 \tan{\left(t \right)} + \operatorname{atan}^{2}{\left(t \right)} - \operatorname{atan}{\left(t \right)}\right) \tan^{\operatorname{atan}{\left(t \right)}}{\left(t \right)}}{\left(t^{2} + 1\right)^{2} \tan^{2}{\left(t \right)}}$$
tan(t)^atan(t)*(atan(t)^2 - atan(t) + 2*tan(t)^3 + 2*tan(t) + t^4*atan(t)^2 + atan(t)^2*tan(t)^4 + log(tan(t))^2*tan(t)^2 + tan(t)^4*atan(t) - t^4*atan(t) - 2*t^2*atan(t) + 2*t^2*atan(t)^2 + 2*t^2*tan(t)^3 + 2*t^2*tan(t) + 2*atan(t)^2*tan(t)^2 + t^4*atan(t)^2*tan(t)^4 + t^4*tan(t)^4*atan(t) - 2*t*tan(t)^2*log(tan(t)) + 2*t^2*atan(t)^2*tan(t)^4 + 2*t^2*tan(t)^4*atan(t) + 2*t^4*atan(t)^2*tan(t)^2 + 2*tan(t)^3*atan(t)*log(tan(t)) + 2*atan(t)*log(tan(t))*tan(t) + 4*t^2*atan(t)^2*tan(t)^2 + 2*t^2*tan(t)^3*atan(t)*log(tan(t)) + 2*t^2*atan(t)*log(tan(t))*tan(t))/((1 + t^2)^2*tan(t)^2)
Respuesta numérica
[src]
tan(t)^atan(t)*((log(tan(t))/(1.0 + t^2) + (1.0 + tan(t)^2)*atan(t)/tan(t))^2 + (2.0 + 2.0*tan(t)^2)*atan(t) + (2.0 + 2.0*tan(t)^2)/((1.0 + t^2)*tan(t)) - (1.0 + tan(t)^2)^2*atan(t)/tan(t)^2 - 2.0*t*log(tan(t))/(1.0 + t^2)^2)
tan(t)^atan(t)*((log(tan(t))/(1.0 + t^2) + (1.0 + tan(t)^2)*atan(t)/tan(t))^2 + (2.0 + 2.0*tan(t)^2)*atan(t) + (2.0 + 2.0*tan(t)^2)/((1.0 + t^2)*tan(t)) - (1.0 + tan(t)^2)^2*atan(t)/tan(t)^2 - 2.0*t*log(tan(t))/(1.0 + t^2)^2)