Integral de 1/(2-3cosx^2) dx
Solución
Solución detallada
Vuelva a escribir el integrando:
1 2 − 3 cos 2 ( x ) = − 1 3 cos 2 ( x ) − 2 \frac{1}{2 - 3 \cos^{2}{\left(x \right)}} = - \frac{1}{3 \cos^{2}{\left(x \right)} - 2} 2 − 3 c o s 2 ( x ) 1 = − 3 c o s 2 ( x ) − 2 1
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 1 3 cos 2 ( x ) − 2 ) d x = − ∫ 1 3 cos 2 ( x ) − 2 d x \int \left(- \frac{1}{3 \cos^{2}{\left(x \right)} - 2}\right)\, dx = - \int \frac{1}{3 \cos^{2}{\left(x \right)} - 2}\, dx ∫ ( − 3 c o s 2 ( x ) − 2 1 ) d x = − ∫ 3 c o s 2 ( x ) − 2 1 d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
− 267 log ( tan ( x 2 ) − 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 log ( tan ( x 2 ) − 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 log ( tan ( x 2 ) + 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 log ( tan ( x 2 ) + 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) − 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) − 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 - \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} − 2376 5 − 2 6 + 970 6 5 − 2 6 267 l o g ( t a n ( 2 x ) − 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 l o g ( t a n ( 2 x ) − 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 l o g ( t a n ( 2 x ) + 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 l o g ( t a n ( 2 x ) + 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) − 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) − 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) + 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) + 2 6 + 5 )
Por lo tanto, el resultado es: 109 6 log ( tan ( x 2 ) − 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 log ( tan ( x 2 ) − 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 log ( tan ( x 2 ) + 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 log ( tan ( x 2 ) + 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) − 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) − 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 l o g ( t a n ( 2 x ) − 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 l o g ( t a n ( 2 x ) − 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) − 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) − 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) + 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 l o g ( t a n ( 2 x ) + 2 6 + 5 )
Ahora simplificar:
109 6 log ( tan ( x 2 ) − 5 − 2 6 ) + 267 log ( tan ( x 2 ) − 5 − 2 6 ) − 267 log ( tan ( x 2 ) + 5 − 2 6 ) − 109 6 log ( tan ( x 2 ) + 5 − 2 6 ) − 267 log ( tan ( x 2 ) − 2 6 + 5 ) − 109 6 log ( tan ( x 2 ) − 2 6 + 5 ) + 109 6 log ( tan ( x 2 ) + 2 6 + 5 ) + 267 log ( tan ( x 2 ) + 2 6 + 5 ) 2 5 − 2 6 ( 1188 + 485 6 ) \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)} + 267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)} - 267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)} - 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)} - 267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)} - 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)} + 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + 267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2 \sqrt{5 - 2 \sqrt{6}} \left(1188 + 485 \sqrt{6}\right)} 2 5 − 2 6 ( 1188 + 485 6 ) 109 6 l o g ( t a n ( 2 x ) − 5 − 2 6 ) + 267 l o g ( t a n ( 2 x ) − 5 − 2 6 ) − 267 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 109 6 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 267 l o g ( t a n ( 2 x ) − 2 6 + 5 ) − 109 6 l o g ( t a n ( 2 x ) − 2 6 + 5 ) + 109 6 l o g ( t a n ( 2 x ) + 2 6 + 5 ) + 267 l o g ( t a n ( 2 x ) + 2 6 + 5 )
Añadimos la constante de integración:
109 6 log ( tan ( x 2 ) − 5 − 2 6 ) + 267 log ( tan ( x 2 ) − 5 − 2 6 ) − 267 log ( tan ( x 2 ) + 5 − 2 6 ) − 109 6 log ( tan ( x 2 ) + 5 − 2 6 ) − 267 log ( tan ( x 2 ) − 2 6 + 5 ) − 109 6 log ( tan ( x 2 ) − 2 6 + 5 ) + 109 6 log ( tan ( x 2 ) + 2 6 + 5 ) + 267 log ( tan ( x 2 ) + 2 6 + 5 ) 2 5 − 2 6 ( 1188 + 485 6 ) + c o n s t a n t \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)} + 267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)} - 267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)} - 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)} - 267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)} - 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)} + 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + 267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2 \sqrt{5 - 2 \sqrt{6}} \left(1188 + 485 \sqrt{6}\right)}+ \mathrm{constant} 2 5 − 2 6 ( 1188 + 485 6 ) 109 6 l o g ( t a n ( 2 x ) − 5 − 2 6 ) + 267 l o g ( t a n ( 2 x ) − 5 − 2 6 ) − 267 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 109 6 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 267 l o g ( t a n ( 2 x ) − 2 6 + 5 ) − 109 6 l o g ( t a n ( 2 x ) − 2 6 + 5 ) + 109 6 l o g ( t a n ( 2 x ) + 2 6 + 5 ) + 267 l o g ( t a n ( 2 x ) + 2 6 + 5 ) + constant
Respuesta:
109 6 log ( tan ( x 2 ) − 5 − 2 6 ) + 267 log ( tan ( x 2 ) − 5 − 2 6 ) − 267 log ( tan ( x 2 ) + 5 − 2 6 ) − 109 6 log ( tan ( x 2 ) + 5 − 2 6 ) − 267 log ( tan ( x 2 ) − 2 6 + 5 ) − 109 6 log ( tan ( x 2 ) − 2 6 + 5 ) + 109 6 log ( tan ( x 2 ) + 2 6 + 5 ) + 267 log ( tan ( x 2 ) + 2 6 + 5 ) 2 5 − 2 6 ( 1188 + 485 6 ) + c o n s t a n t \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)} + 267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)} - 267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)} - 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)} - 267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)} - 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)} + 109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + 267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2 \sqrt{5 - 2 \sqrt{6}} \left(1188 + 485 \sqrt{6}\right)}+ \mathrm{constant} 2 5 − 2 6 ( 1188 + 485 6 ) 109 6 l o g ( t a n ( 2 x ) − 5 − 2 6 ) + 267 l o g ( t a n ( 2 x ) − 5 − 2 6 ) − 267 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 109 6 l o g ( t a n ( 2 x ) + 5 − 2 6 ) − 267 l o g ( t a n ( 2 x ) − 2 6 + 5 ) − 109 6 l o g ( t a n ( 2 x ) − 2 6 + 5 ) + 109 6 l o g ( t a n ( 2 x ) + 2 6 + 5 ) + 267 l o g ( t a n ( 2 x ) + 2 6 + 5 ) + constant
Respuesta (Indefinida)
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/ | / ___ /x\| | / ___ /x\| ___ | / ___ /x\| ___ | / ___ /x\| / ___ / ___ | / ___ /x\| / ___ / ___ | / ___ /x\| ___ / ___ / ___ | / ___ /x\| ___ / ___ / ___ | / ___ /x\|
| 267*log|\/ 5 - 2*\/ 6 + tan|-|| 267*log|- \/ 5 - 2*\/ 6 + tan|-|| 109*\/ 6 *log|\/ 5 - 2*\/ 6 + tan|-|| 109*\/ 6 *log|- \/ 5 - 2*\/ 6 + tan|-|| 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|- \/ 5 + 2*\/ 6 + tan|-|| 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|\/ 5 + 2*\/ 6 + tan|-|| 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|- \/ 5 + 2*\/ 6 + tan|-|| 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|\/ 5 + 2*\/ 6 + tan|-||
| 1 \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2//
| ------------- dx = C - -------------------------------------------------- + -------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------- - ---------------------------------------------------------------------- + -------------------------------------------------------------------- - ---------------------------------------------------------------------------- + --------------------------------------------------------------------------
| 2 _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________
| 2 - 3*cos (x) / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
| 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6
/
∫ 1 2 − 3 cos 2 ( x ) d x = C + 109 6 log ( tan ( x 2 ) − 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 log ( tan ( x 2 ) − 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 log ( tan ( x 2 ) + 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 log ( tan ( x 2 ) + 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) − 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) − 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 log ( tan ( x 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 \int \frac{1}{2 - 3 \cos^{2}{\left(x \right)}}\, dx = C + \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} ∫ 2 − 3 cos 2 ( x ) 1 d x = C + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( tan ( 2 x ) − 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( tan ( 2 x ) − 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( tan ( 2 x ) + 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( tan ( 2 x ) + 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 log ( tan ( 2 x ) − 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 log ( tan ( 2 x ) − 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 log ( tan ( 2 x ) + 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 log ( tan ( 2 x ) + 2 6 + 5 )
Gráfica
0.00 1.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 -10000 10000
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| | / ___ || | / ___ | | / ___ | | / ___ | ___ | | / ___ || ___ | / ___ | ___ | / ___ | ___ | / ___ | / ___ / ___ | | / ___ || / ___ / ___ | / ___ | / ___ / ___ | | / ___ || / ___ / ___ | / ___ | ___ / ___ / ___ | | / ___ || ___ / ___ / ___ | / ___ | ___ / ___ / ___ | | / ___ || ___ / ___ / ___ | / ___ |
267*\pi*I + log\\/ 5 - 2*\/ 6 // 267*log\\/ 5 - 2*\/ 6 + tan(1/2)/ 267*log\\/ 5 - 2*\/ 6 / 267*log\- \/ 5 - 2*\/ 6 + tan(1/2)/ 109*\/ 6 *\pi*I + log\\/ 5 - 2*\/ 6 // 109*\/ 6 *log\\/ 5 - 2*\/ 6 + tan(1/2)/ 109*\/ 6 *log\\/ 5 - 2*\/ 6 / 109*\/ 6 *log\- \/ 5 - 2*\/ 6 + tan(1/2)/ 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 - tan(1/2)// 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 / 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 // 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 + tan(1/2)/ 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 - tan(1/2)// 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 / 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 // 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 + tan(1/2)/
- -------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- - -------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- - ------------------------------------------------------------------------------- - ----------------------------------------------------------- + -------------------------------------------------------------------- + ---------------------------------------------------------------------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------- + -------------------------------------------------------------------------- + ----------------------------------------------------------------------------
_____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________
/ ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6
267 log ( − 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 log ( − 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 log ( 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 log ( 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 log ( 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 log ( 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 log ( tan ( 1 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 log ( tan ( 1 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 ( log ( − tan ( 1 2 ) + 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 ( log ( 5 − 2 6 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 ( log ( − tan ( 1 2 ) + 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 ( log ( 5 − 2 6 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 \frac{267 \log{\left(- \sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \log{\left(- \sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \log{\left(\sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \log{\left(\sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \log{\left(\sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \log{\left(\sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \left(\log{\left(\sqrt{5 - 2 \sqrt{6}} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \left(\log{\left(\sqrt{5 - 2 \sqrt{6}} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(\sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(\sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( − 5 − 2 6 + tan ( 2 1 ) ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( − 5 − 2 6 + tan ( 2 1 ) ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( 5 − 2 6 + tan ( 2 1 ) ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( 5 − 2 6 + tan ( 2 1 ) ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 log ( tan ( 2 1 ) + 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 log ( tan ( 2 1 ) + 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 ( log ( − tan ( 2 1 ) + 2 6 + 5 ) + iπ ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 ( log ( 5 − 2 6 ) + iπ ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 ( log ( − tan ( 2 1 ) + 2 6 + 5 ) + iπ ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 ( log ( 5 − 2 6 ) + iπ ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + iπ ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + iπ )
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| | / ___ || | / ___ | | / ___ | | / ___ | ___ | | / ___ || ___ | / ___ | ___ | / ___ | ___ | / ___ | / ___ / ___ | | / ___ || / ___ / ___ | / ___ | / ___ / ___ | | / ___ || / ___ / ___ | / ___ | ___ / ___ / ___ | | / ___ || ___ / ___ / ___ | / ___ | ___ / ___ / ___ | | / ___ || ___ / ___ / ___ | / ___ |
267*\pi*I + log\\/ 5 - 2*\/ 6 // 267*log\\/ 5 - 2*\/ 6 + tan(1/2)/ 267*log\\/ 5 - 2*\/ 6 / 267*log\- \/ 5 - 2*\/ 6 + tan(1/2)/ 109*\/ 6 *\pi*I + log\\/ 5 - 2*\/ 6 // 109*\/ 6 *log\\/ 5 - 2*\/ 6 + tan(1/2)/ 109*\/ 6 *log\\/ 5 - 2*\/ 6 / 109*\/ 6 *log\- \/ 5 - 2*\/ 6 + tan(1/2)/ 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 - tan(1/2)// 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 / 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 // 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 + tan(1/2)/ 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 - tan(1/2)// 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 / 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *\pi*I + log\\/ 5 + 2*\/ 6 // 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log\\/ 5 + 2*\/ 6 + tan(1/2)/
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_____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________
/ ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6
267 log ( − 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 log ( − 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 log ( 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 log ( 5 − 2 6 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 log ( 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 log ( 5 − 2 6 + tan ( 1 2 ) ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 log ( tan ( 1 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 log ( tan ( 1 2 ) + 2 6 + 5 ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 5 − 2 6 2 6 + 5 ( log ( − tan ( 1 2 ) + 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 267 ( log ( 5 − 2 6 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 5 − 2 6 2 6 + 5 ( log ( − tan ( 1 2 ) + 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 − 109 6 ( log ( 5 − 2 6 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 109 6 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 + 267 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + i π ) 2376 5 − 2 6 + 970 6 5 − 2 6 \frac{267 \log{\left(- \sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \log{\left(- \sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \log{\left(\sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \log{\left(\sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \log{\left(\sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \log{\left(\sqrt{5 - 2 \sqrt{6}} + \tan{\left(\frac{1}{2} \right)} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \left(\log{\left(\sqrt{5 - 2 \sqrt{6}} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \left(\log{\left(\sqrt{5 - 2 \sqrt{6}} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(\sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \left(\log{\left(\sqrt{2 \sqrt{6} + 5} \right)} + i \pi\right)}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( − 5 − 2 6 + tan ( 2 1 ) ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( − 5 − 2 6 + tan ( 2 1 ) ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( 5 − 2 6 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( 5 − 2 6 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 log ( 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 log ( 5 − 2 6 + tan ( 2 1 ) ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 log ( 5 − 2 6 + tan ( 2 1 ) ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 log ( tan ( 2 1 ) + 2 6 + 5 ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 log ( tan ( 2 1 ) + 2 6 + 5 ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 ( log ( − tan ( 2 1 ) + 2 6 + 5 ) + iπ ) − 2376 5 − 2 6 + 970 6 5 − 2 6 267 ( log ( 5 − 2 6 ) + iπ ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 ( log ( − tan ( 2 1 ) + 2 6 + 5 ) + iπ ) − 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 ( log ( 5 − 2 6 ) + iπ ) + 2376 5 − 2 6 + 970 6 5 − 2 6 109 6 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + iπ ) + 2376 5 − 2 6 + 970 6 5 − 2 6 267 5 − 2 6 2 6 + 5 ( log ( 2 6 + 5 ) + iπ )
-267*(pi*i + log(sqrt(5 - 2*sqrt(6))))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 267*log(sqrt(5 - 2*sqrt(6)) + tan(1/2))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 267*log(sqrt(5 - 2*sqrt(6)))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 267*log(-sqrt(5 - 2*sqrt(6)) + tan(1/2))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 109*sqrt(6)*(pi*i + log(sqrt(5 - 2*sqrt(6))))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 109*sqrt(6)*log(sqrt(5 - 2*sqrt(6)) + tan(1/2))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 109*sqrt(6)*log(sqrt(5 - 2*sqrt(6)))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 109*sqrt(6)*log(-sqrt(5 - 2*sqrt(6)) + tan(1/2))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 267*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*(pi*i + log(sqrt(5 + 2*sqrt(6)) - tan(1/2)))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 267*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*log(sqrt(5 + 2*sqrt(6)))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 267*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*(pi*i + log(sqrt(5 + 2*sqrt(6))))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 267*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*log(sqrt(5 + 2*sqrt(6)) + tan(1/2))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 109*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*(pi*i + log(sqrt(5 + 2*sqrt(6)) - tan(1/2)))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) - 109*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*log(sqrt(5 + 2*sqrt(6)))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 109*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*(pi*i + log(sqrt(5 + 2*sqrt(6))))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6))) + 109*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(5 + 2*sqrt(6))*log(sqrt(5 + 2*sqrt(6)) + tan(1/2))/(2376*sqrt(5 - 2*sqrt(6)) + 970*sqrt(6)*sqrt(5 - 2*sqrt(6)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.