Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(3)*(192*sin(8*x)+6*(3*sin(8*x)+16*x*cos(8*x))/x^2+1024*x*cos(8*x)+(3*sin(8*x)^2-576*x^2*sin(8*x)^2+576*x^2*cos(8*x)^2-2048*x^3*cos(8*x)*sin(8*x)+144*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x))-6*(3*sin(8*x)^2-64*x^2*sin(8*x)^2+64*x^2*cos(8*x)^2+48*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x))+192*cos(8*x)^2*(3*sin(8*x)+16*x*cos(8*x))/sin(8*x)^2-32*(3*sin(8*x)^2-64*x^2*sin(8*x)^2+64*x^2*cos(8*x)^2+48*x*cos(8*x)*sin(8*x))*cos(8*x)/(x*sin(8*x)^2)+48*(3*sin(8*x)+16*x*cos(8*x))*cos(8*x)/(x*sin(8*x))+3*(3*sin(8*x)+16*x*cos(8*x))^3/(8*x^2*log(x^3*sin(8*x)^2)^2*sin(8*x)^2)+9*(3*sin(8*x)+16*x*cos(8*x))^2/(4*x^2*log(x^3*sin(8*x)^2)*sin(8*x))+12*(3*sin(8*x)+16*x*cos(8*x))^2*cos(8*x)/(x*log(x^3*sin(8*x)^2)*sin(8*x)^2)-3*(3*sin(8*x)+16*x*cos(8*x))*(3*sin(8*x)^2-64*x^2*sin(8*x)^2+64*x^2*cos(8*x)^2+48*x*cos(8*x)*sin(8*x))/(2*x^2*log(x^3*sin(8*x)^2)*sin(8*x)^2))/(x*sqrt(log(x^3*sin(8*x)^2))*sin(8*x))
¿Cómo vas a descomponer esta sqrt(3)*(192*sin(8*x)+6*(3*sin(8*x)+16*x*cos(8*x))/x^2+1024*x*cos(8*x)+(3*sin(8*x)^2-576*x^2*sin(8*x)^2+576*x^2*cos(8*x)^2-2048*x^3*cos(8*x)*sin(8*x)+144*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x))-6*(3*sin(8*x)^2-64*x^2*sin(8*x)^2+64*x^2*cos(8*x)^2+48*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x))+192*cos(8*x)^2*(3*sin(8*x)+16*x*cos(8*x))/sin(8*x)^2-32*(3*sin(8*x)^2-64*x^2*sin(8*x)^2+64*x^2*cos(8*x)^2+48*x*cos(8*x)*sin(8*x))*cos(8*x)/(x*sin(8*x)^2)+48*(3*sin(8*x)+16*x*cos(8*x))*cos(8*x)/(x*sin(8*x))+3*(3*sin(8*x)+16*x*cos(8*x))^3/(8*x^2*log(x^3*sin(8*x)^2)^2*sin(8*x)^2)+9*(3*sin(8*x)+16*x*cos(8*x))^2/(4*x^2*log(x^3*sin(8*x)^2)*sin(8*x))+12*(3*sin(8*x)+16*x*cos(8*x))^2*cos(8*x)/(x*log(x^3*sin(8*x)^2)*sin(8*x)^2)-3*(3*sin(8*x)+16*x*cos(8*x))*(3*sin(8*x)^2-64*x^2*sin(8*x)^2+64*x^2*cos(8*x)^2+48*x*cos(8*x)*sin(8*x))/(2*x^2*log(x^3*sin(8*x)^2)*sin(8*x)^2))/(x*sqrt(log(x^3*sin(8*x)^2))*sin(8*x)) expresión en fracciones?
Solución
Ha introducido
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/ 2 2 2 2 2 3 / 2 2 2 2 2 \ 2 / 2 2 2 2 2 \ 3 2 2 / 2 2 2 2 2 \\
___ | 6*(3*sin(8*x) + 16*x*cos(8*x)) 3*sin (8*x) - 576*x *sin (8*x) + 576*x *cos (8*x) - 2048*x *cos(8*x)*sin(8*x) + 144*x*cos(8*x)*sin(8*x) 6*\3*sin (8*x) - 64*x *sin (8*x) + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/ 192*cos (8*x)*(3*sin(8*x) + 16*x*cos(8*x)) 32*\3*sin (8*x) - 64*x *sin (8*x) + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/*cos(8*x) 48*(3*sin(8*x) + 16*x*cos(8*x))*cos(8*x) 3*(3*sin(8*x) + 16*x*cos(8*x)) 9*(3*sin(8*x) + 16*x*cos(8*x)) 12*(3*sin(8*x) + 16*x*cos(8*x)) *cos(8*x) 3*(3*sin(8*x) + 16*x*cos(8*x))*\3*sin (8*x) - 64*x *sin (8*x) + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/|
\/ 3 *|192*sin(8*x) + ------------------------------ + 1024*x*cos(8*x) + ------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------- + ------------------------------------------ - -------------------------------------------------------------------------------------- + ---------------------------------------- + --------------------------------- + ------------------------------- + ----------------------------------------- - ---------------------------------------------------------------------------------------------------------|
| 2 2 2 2 2 x*sin(8*x) 2 2/ 3 2 \ 2 2 / 3 2 \ / 3 2 \ 2 2 / 3 2 \ 2 |
\ x x *sin(8*x) x *sin(8*x) sin (8*x) x*sin (8*x) 8*x *log \x *sin (8*x)/*sin (8*x) 4*x *log\x *sin (8*x)/*sin(8*x) x*log\x *sin (8*x)/*sin (8*x) 2*x *log\x *sin (8*x)/*sin (8*x) /
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___________________
/ / 3 2 \
x*\/ log\x *sin (8*x)/ *sin(8*x)
$$\frac{\sqrt{3} \left(\left(\left(\left(\left(\left(\left(\frac{\left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) 192 \cos^{2}{\left(8 x \right)}}{\sin^{2}{\left(8 x \right)}} + \left(\left(\left(1024 x \cos{\left(8 x \right)} + \left(192 \sin{\left(8 x \right)} + \frac{6 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)}{x^{2}}\right)\right) + \frac{144 x \cos{\left(8 x \right)} \sin{\left(8 x \right)} + \left(- 2048 x^{3} \cos{\left(8 x \right)} \sin{\left(8 x \right)} + \left(576 x^{2} \cos^{2}{\left(8 x \right)} + \left(- 576 x^{2} \sin^{2}{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)\right)\right)}{x^{2} \sin{\left(8 x \right)}}\right) - \frac{6 \left(48 x \cos{\left(8 x \right)} \sin{\left(8 x \right)} + \left(64 x^{2} \cos^{2}{\left(8 x \right)} + \left(- 64 x^{2} \sin^{2}{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)\right)\right)}{x^{2} \sin{\left(8 x \right)}}\right)\right) - \frac{32 \left(48 x \cos{\left(8 x \right)} \sin{\left(8 x \right)} + \left(64 x^{2} \cos^{2}{\left(8 x \right)} + \left(- 64 x^{2} \sin^{2}{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)\right)\right) \cos{\left(8 x \right)}}{x \sin^{2}{\left(8 x \right)}}\right) + \frac{48 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin{\left(8 x \right)}}\right) + \frac{3 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{3}}{8 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)}}\right) + \frac{9 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2}}{4 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)}}\right) + \frac{12 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2} \cos{\left(8 x \right)}}{x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}}\right) - \frac{3 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \left(48 x \cos{\left(8 x \right)} \sin{\left(8 x \right)} + \left(64 x^{2} \cos^{2}{\left(8 x \right)} + \left(- 64 x^{2} \sin^{2}{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)\right)\right)}{2 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}}\right)}{x \sqrt{\log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}} \sin{\left(8 x \right)}}$$
(sqrt(3)*(192*sin(8*x) + (6*(3*sin(8*x) + (16*x)*cos(8*x)))/x^2 + (1024*x)*cos(8*x) + (3*sin(8*x)^2 - 576*x^2*sin(8*x)^2 + (576*x^2)*cos(8*x)^2 - (2048*x^3)*cos(8*x)*sin(8*x) + ((144*x)*cos(8*x))*sin(8*x))/((x^2*sin(8*x))) - 6*(3*sin(8*x)^2 - 64*x^2*sin(8*x)^2 + (64*x^2)*cos(8*x)^2 + ((48*x)*cos(8*x))*sin(8*x))/(x^2*sin(8*x)) + ((192*cos(8*x)^2)*(3*sin(8*x) + (16*x)*cos(8*x)))/sin(8*x)^2 - (32*(3*sin(8*x)^2 - 64*x^2*sin(8*x)^2 + (64*x^2)*cos(8*x)^2 + ((48*x)*cos(8*x))*sin(8*x)))*cos(8*x)/(x*sin(8*x)^2) + ((48*(3*sin(8*x) + (16*x)*cos(8*x)))*cos(8*x))/((x*sin(8*x))) + (3*(3*sin(8*x) + (16*x)*cos(8*x))^3)/((((8*x^2)*log(x^3*sin(8*x)^2)^2)*sin(8*x)^2)) + (9*(3*sin(8*x) + (16*x)*cos(8*x))^2)/((((4*x^2)*log(x^3*sin(8*x)^2))*sin(8*x))) + ((12*(3*sin(8*x) + (16*x)*cos(8*x))^2)*cos(8*x))/(((x*log(x^3*sin(8*x)^2))*sin(8*x)^2)) - (3*(3*sin(8*x) + (16*x)*cos(8*x)))*(3*sin(8*x)^2 - 64*x^2*sin(8*x)^2 + (64*x^2)*cos(8*x)^2 + ((48*x)*cos(8*x))*sin(8*x))/(((2*x^2)*log(x^3*sin(8*x)^2))*sin(8*x)^2)))/(((x*sqrt(log(x^3*sin(8*x)^2)))*sin(8*x)))
Simplificación general
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___ / 3 2/ 3 2 \ 3 3 / 3 2 \ 3 3 2 2 3 / 3 2 \ 2 2 3 3 2/ 3 2 \ 3 3 / 3 2 \ 2 / 3 2 \ 2 2 / 3 2 \ 3 2/ 3 2 \ 2 3 2 / 3 2 \\
\/ 3 *\81*sin (8*x) + 24*log \x *sin (8*x)/*sin (8*x) + 54*sin (8*x)*log\x *sin (8*x)/ + 12288*x *cos (8*x) + 1296*x*sin (8*x)*cos(8*x) + 2304*x *sin (8*x)*log\x *sin (8*x)/ + 6912*x *cos (8*x)*sin(8*x) + 8192*x *cos (8*x)*log \x *sin (8*x)/ + 12288*x *cos (8*x)*log\x *sin (8*x)/ + 288*x*sin (8*x)*cos(8*x)*log\x *sin (8*x)/ + 2304*x *cos (8*x)*log\x *sin (8*x)/*sin(8*x) + 8192*x *log \x *sin (8*x)/*sin (8*x)*cos(8*x) + 12288*x *sin (8*x)*cos(8*x)*log\x *sin (8*x)//
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3 5/2/ 3 2 \ 3
8*x *log \x *sin (8*x)/*sin (8*x)
$$\frac{\sqrt{3} \left(8192 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 8192 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \cos^{3}{\left(8 x \right)} + 12288 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 12288 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \cos^{3}{\left(8 x \right)} + 12288 x^{3} \cos^{3}{\left(8 x \right)} + 2304 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{3}{\left(8 x \right)} + 2304 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} + 6912 x^{2} \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} + 288 x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 1296 x \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 24 \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{3}{\left(8 x \right)} + 54 \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{3}{\left(8 x \right)} + 81 \sin^{3}{\left(8 x \right)}\right)}{8 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{\frac{5}{2}} \sin^{3}{\left(8 x \right)}}$$
sqrt(3)*(81*sin(8*x)^3 + 24*log(x^3*sin(8*x)^2)^2*sin(8*x)^3 + 54*sin(8*x)^3*log(x^3*sin(8*x)^2) + 12288*x^3*cos(8*x)^3 + 1296*x*sin(8*x)^2*cos(8*x) + 2304*x^2*sin(8*x)^3*log(x^3*sin(8*x)^2) + 6912*x^2*cos(8*x)^2*sin(8*x) + 8192*x^3*cos(8*x)^3*log(x^3*sin(8*x)^2)^2 + 12288*x^3*cos(8*x)^3*log(x^3*sin(8*x)^2) + 288*x*sin(8*x)^2*cos(8*x)*log(x^3*sin(8*x)^2) + 2304*x^2*cos(8*x)^2*log(x^3*sin(8*x)^2)*sin(8*x) + 8192*x^3*log(x^3*sin(8*x)^2)^2*sin(8*x)^2*cos(8*x) + 12288*x^3*sin(8*x)^2*cos(8*x)*log(x^3*sin(8*x)^2))/(8*x^3*log(x^3*sin(8*x)^2)^(5/2)*sin(8*x)^3)
Respuesta numérica
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log(x^3*sin(8*x)^2)^(-0.5)*(332.553755053224*sin(8*x) + 1.73205080756888*(18.0*sin(8*x) + 96.0*x*cos(8*x))/x^2 + 1773.62002695053*x*cos(8*x) + 332.553755053224*cos(8*x)^2*(3.0*sin(8*x) + 16.0*x*cos(8*x))/sin(8*x)^2 + 1.73205080756888*(3.0*sin(8*x)^2 + 576.0*x^2*cos(8*x)^2 - 576.0*x^2*sin(8*x)^2 + 144.0*x*cos(8*x)*sin(8*x) - 2048.0*x^3*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) - 1.73205080756888*(18.0*sin(8*x)^2 + 384.0*x^2*cos(8*x)^2 - 384.0*x^2*sin(8*x)^2 + 288.0*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) + 2660.4300404258*(0.1875*sin(8*x) + x*cos(8*x))^3/(x^2*log(x^3*sin(8*x)^2)^2*sin(8*x)^2) + 1.73205080756888*(144.0*sin(8*x) + 768.0*x*cos(8*x))*cos(8*x)/(x*sin(8*x)) + 997.661265159673*(0.1875*sin(8*x) + x*cos(8*x))^2/(x^2*log(x^3*sin(8*x)^2)*sin(8*x)) - 1.73205080756888*(96.0*sin(8*x)^2 + 2048.0*x^2*cos(8*x)^2 - 2048.0*x^2*sin(8*x)^2 + 1536.0*x*cos(8*x)*sin(8*x))*cos(8*x)/(x*sin(8*x)^2) + 5320.86008085159*(0.1875*sin(8*x) + x*cos(8*x))^2*cos(8*x)/(x*log(x^3*sin(8*x)^2)*sin(8*x)^2) - 0.866025403784439*(9.0*sin(8*x) + 48.0*x*cos(8*x))*(3.0*sin(8*x)^2 + 64.0*x^2*cos(8*x)^2 - 64.0*x^2*sin(8*x)^2 + 48.0*x*cos(8*x)*sin(8*x))/(x^2*log(x^3*sin(8*x)^2)*sin(8*x)^2))/(x*sin(8*x))
log(x^3*sin(8*x)^2)^(-0.5)*(332.553755053224*sin(8*x) + 1.73205080756888*(18.0*sin(8*x) + 96.0*x*cos(8*x))/x^2 + 1773.62002695053*x*cos(8*x) + 332.553755053224*cos(8*x)^2*(3.0*sin(8*x) + 16.0*x*cos(8*x))/sin(8*x)^2 + 1.73205080756888*(3.0*sin(8*x)^2 + 576.0*x^2*cos(8*x)^2 - 576.0*x^2*sin(8*x)^2 + 144.0*x*cos(8*x)*sin(8*x) - 2048.0*x^3*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) - 1.73205080756888*(18.0*sin(8*x)^2 + 384.0*x^2*cos(8*x)^2 - 384.0*x^2*sin(8*x)^2 + 288.0*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) + 2660.4300404258*(0.1875*sin(8*x) + x*cos(8*x))^3/(x^2*log(x^3*sin(8*x)^2)^2*sin(8*x)^2) + 1.73205080756888*(144.0*sin(8*x) + 768.0*x*cos(8*x))*cos(8*x)/(x*sin(8*x)) + 997.661265159673*(0.1875*sin(8*x) + x*cos(8*x))^2/(x^2*log(x^3*sin(8*x)^2)*sin(8*x)) - 1.73205080756888*(96.0*sin(8*x)^2 + 2048.0*x^2*cos(8*x)^2 - 2048.0*x^2*sin(8*x)^2 + 1536.0*x*cos(8*x)*sin(8*x))*cos(8*x)/(x*sin(8*x)^2) + 5320.86008085159*(0.1875*sin(8*x) + x*cos(8*x))^2*cos(8*x)/(x*log(x^3*sin(8*x)^2)*sin(8*x)^2) - 0.866025403784439*(9.0*sin(8*x) + 48.0*x*cos(8*x))*(3.0*sin(8*x)^2 + 64.0*x^2*cos(8*x)^2 - 64.0*x^2*sin(8*x)^2 + 48.0*x*cos(8*x)*sin(8*x))/(x^2*log(x^3*sin(8*x)^2)*sin(8*x)^2))/(x*sin(8*x))
Combinatoria
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___ / 3 2/ 3 2 \ 3 3 / 3 2 \ 3 3 2 2 3 / 3 2 \ 2 2 3 3 2/ 3 2 \ 3 3 / 3 2 \ 2 / 3 2 \ 2 2 / 3 2 \ 3 2/ 3 2 \ 2 3 2 / 3 2 \\
\/ 3 *\81*sin (8*x) + 24*log \x *sin (8*x)/*sin (8*x) + 54*sin (8*x)*log\x *sin (8*x)/ + 12288*x *cos (8*x) + 1296*x*sin (8*x)*cos(8*x) + 2304*x *sin (8*x)*log\x *sin (8*x)/ + 6912*x *cos (8*x)*sin(8*x) + 8192*x *cos (8*x)*log \x *sin (8*x)/ + 12288*x *cos (8*x)*log\x *sin (8*x)/ + 288*x*sin (8*x)*cos(8*x)*log\x *sin (8*x)/ + 2304*x *cos (8*x)*log\x *sin (8*x)/*sin(8*x) + 8192*x *log \x *sin (8*x)/*sin (8*x)*cos(8*x) + 12288*x *sin (8*x)*cos(8*x)*log\x *sin (8*x)//
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3 5/2/ 3 2 \ 3
8*x *log \x *sin (8*x)/*sin (8*x)
$$\frac{\sqrt{3} \left(8192 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 8192 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \cos^{3}{\left(8 x \right)} + 12288 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 12288 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \cos^{3}{\left(8 x \right)} + 12288 x^{3} \cos^{3}{\left(8 x \right)} + 2304 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{3}{\left(8 x \right)} + 2304 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} + 6912 x^{2} \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} + 288 x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 1296 x \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 24 \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{3}{\left(8 x \right)} + 54 \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{3}{\left(8 x \right)} + 81 \sin^{3}{\left(8 x \right)}\right)}{8 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{\frac{5}{2}} \sin^{3}{\left(8 x \right)}}$$
sqrt(3)*(81*sin(8*x)^3 + 24*log(x^3*sin(8*x)^2)^2*sin(8*x)^3 + 54*sin(8*x)^3*log(x^3*sin(8*x)^2) + 12288*x^3*cos(8*x)^3 + 1296*x*sin(8*x)^2*cos(8*x) + 2304*x^2*sin(8*x)^3*log(x^3*sin(8*x)^2) + 6912*x^2*cos(8*x)^2*sin(8*x) + 8192*x^3*cos(8*x)^3*log(x^3*sin(8*x)^2)^2 + 12288*x^3*cos(8*x)^3*log(x^3*sin(8*x)^2) + 288*x*sin(8*x)^2*cos(8*x)*log(x^3*sin(8*x)^2) + 2304*x^2*cos(8*x)^2*log(x^3*sin(8*x)^2)*sin(8*x) + 8192*x^3*log(x^3*sin(8*x)^2)^2*sin(8*x)^2*cos(8*x) + 12288*x^3*sin(8*x)^2*cos(8*x)*log(x^3*sin(8*x)^2))/(8*x^3*log(x^3*sin(8*x)^2)^(5/2)*sin(8*x)^3)
Denominador común
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___ 3 ___ 2/ 3 2 \ 3 ___ 3 / 3 2 \ ___ 3 3 ___ 2 ___ 2 3 / 3 2 \ ___ 2 2 ___ 3 3 2/ 3 2 \ ___ 3 3 / 3 2 \ ___ 2 / 3 2 \ ___ 2 2 / 3 2 \ ___ 3 2/ 3 2 \ 2 ___ 3 2 / 3 2 \
81*\/ 3 *sin (8*x) + 24*\/ 3 *log \x *sin (8*x)/*sin (8*x) + 54*\/ 3 *sin (8*x)*log\x *sin (8*x)/ + 12288*\/ 3 *x *cos (8*x) + 1296*x*\/ 3 *sin (8*x)*cos(8*x) + 2304*\/ 3 *x *sin (8*x)*log\x *sin (8*x)/ + 6912*\/ 3 *x *cos (8*x)*sin(8*x) + 8192*\/ 3 *x *cos (8*x)*log \x *sin (8*x)/ + 12288*\/ 3 *x *cos (8*x)*log\x *sin (8*x)/ + 288*x*\/ 3 *sin (8*x)*cos(8*x)*log\x *sin (8*x)/ + 2304*\/ 3 *x *cos (8*x)*log\x *sin (8*x)/*sin(8*x) + 8192*\/ 3 *x *log \x *sin (8*x)/*sin (8*x)*cos(8*x) + 12288*\/ 3 *x *sin (8*x)*cos(8*x)*log\x *sin (8*x)/
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3 5/2/ 3 2 \ 3
8*x *log \x *sin (8*x)/*sin (8*x)
$$\frac{8192 \sqrt{3} x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 8192 \sqrt{3} x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \cos^{3}{\left(8 x \right)} + 12288 \sqrt{3} x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 12288 \sqrt{3} x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \cos^{3}{\left(8 x \right)} + 12288 \sqrt{3} x^{3} \cos^{3}{\left(8 x \right)} + 2304 \sqrt{3} x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{3}{\left(8 x \right)} + 2304 \sqrt{3} x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} + 6912 \sqrt{3} x^{2} \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} + 288 \sqrt{3} x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 1296 \sqrt{3} x \sin^{2}{\left(8 x \right)} \cos{\left(8 x \right)} + 24 \sqrt{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{3}{\left(8 x \right)} + 54 \sqrt{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{3}{\left(8 x \right)} + 81 \sqrt{3} \sin^{3}{\left(8 x \right)}}{8 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{\frac{5}{2}} \sin^{3}{\left(8 x \right)}}$$
(81*sqrt(3)*sin(8*x)^3 + 24*sqrt(3)*log(x^3*sin(8*x)^2)^2*sin(8*x)^3 + 54*sqrt(3)*sin(8*x)^3*log(x^3*sin(8*x)^2) + 12288*sqrt(3)*x^3*cos(8*x)^3 + 1296*x*sqrt(3)*sin(8*x)^2*cos(8*x) + 2304*sqrt(3)*x^2*sin(8*x)^3*log(x^3*sin(8*x)^2) + 6912*sqrt(3)*x^2*cos(8*x)^2*sin(8*x) + 8192*sqrt(3)*x^3*cos(8*x)^3*log(x^3*sin(8*x)^2)^2 + 12288*sqrt(3)*x^3*cos(8*x)^3*log(x^3*sin(8*x)^2) + 288*x*sqrt(3)*sin(8*x)^2*cos(8*x)*log(x^3*sin(8*x)^2) + 2304*sqrt(3)*x^2*cos(8*x)^2*log(x^3*sin(8*x)^2)*sin(8*x) + 8192*sqrt(3)*x^3*log(x^3*sin(8*x)^2)^2*sin(8*x)^2*cos(8*x) + 12288*sqrt(3)*x^3*sin(8*x)^2*cos(8*x)*log(x^3*sin(8*x)^2))/(8*x^3*log(x^3*sin(8*x)^2)^(5/2)*sin(8*x)^3)
Unión de expresiones racionales
[src]
___ / 3 2/ 3 2 \ // 2 / 2\ / 2 3 \ 2 / 2\ 2 2 3 \ / 2 / 2\ 2 2 \ 2 2 \ / 2 / 2\ 2 2 \ / 3 2 \ 2 / 3 2 \ 2 / 3 2 \\
\/ 3 *\3*(3*sin(8*x) + 16*x*cos(8*x)) + 8*log \x *sin (8*x)/*\\- 6*sin (8*x)*\3 - 64*x / + 2*\9*sin(8*x) + 48*x*cos(8*x) + 96*x *sin(8*x) + 512*x *cos(8*x)/*sin(8*x) + 3*sin (8*x)*\1 - 192*x / + 192*x *cos (8*x) - 2048*x *cos(8*x)*sin(8*x) - 144*x*cos(8*x)*sin(8*x)/*sin(8*x) - 32*x*\sin (8*x)*\3 - 64*x / + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/*cos(8*x) + 192*x *cos (8*x)*(3*sin(8*x) + 16*x*cos(8*x)) + 48*x*(3*sin(8*x) + 16*x*cos(8*x))*cos(8*x)*sin(8*x)/ - 12*(3*sin(8*x) + 16*x*cos(8*x))*\sin (8*x)*\3 - 64*x / + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/*log\x *sin (8*x)/ + 18*(3*sin(8*x) + 16*x*cos(8*x)) *log\x *sin (8*x)/*sin(8*x) + 96*x*(3*sin(8*x) + 16*x*cos(8*x)) *cos(8*x)*log\x *sin (8*x)//
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3 5/2/ 3 2 \ 3
8*x *log \x *sin (8*x)/*sin (8*x)
$$\frac{\sqrt{3} \left(96 x \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \cos{\left(8 x \right)} + 3 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{3} + 18 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)} - 12 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \left(64 x^{2} \cos^{2}{\left(8 x \right)} + 48 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + \left(3 - 64 x^{2}\right) \sin^{2}{\left(8 x \right)}\right) \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} + 8 \left(192 x^{2} \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \cos^{2}{\left(8 x \right)} + 48 x \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \sin{\left(8 x \right)} \cos{\left(8 x \right)} - 32 x \left(64 x^{2} \cos^{2}{\left(8 x \right)} + 48 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + \left(3 - 64 x^{2}\right) \sin^{2}{\left(8 x \right)}\right) \cos{\left(8 x \right)} + \left(- 2048 x^{3} \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 192 x^{2} \cos^{2}{\left(8 x \right)} - 144 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \left(1 - 192 x^{2}\right) \sin^{2}{\left(8 x \right)} - 6 \left(3 - 64 x^{2}\right) \sin^{2}{\left(8 x \right)} + 2 \left(512 x^{3} \cos{\left(8 x \right)} + 96 x^{2} \sin{\left(8 x \right)} + 48 x \cos{\left(8 x \right)} + 9 \sin{\left(8 x \right)}\right) \sin{\left(8 x \right)}\right) \sin{\left(8 x \right)}\right) \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2}\right)}{8 x^{3} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{\frac{5}{2}} \sin^{3}{\left(8 x \right)}}$$
sqrt(3)*(3*(3*sin(8*x) + 16*x*cos(8*x))^3 + 8*log(x^3*sin(8*x)^2)^2*((-6*sin(8*x)^2*(3 - 64*x^2) + 2*(9*sin(8*x) + 48*x*cos(8*x) + 96*x^2*sin(8*x) + 512*x^3*cos(8*x))*sin(8*x) + 3*sin(8*x)^2*(1 - 192*x^2) + 192*x^2*cos(8*x)^2 - 2048*x^3*cos(8*x)*sin(8*x) - 144*x*cos(8*x)*sin(8*x))*sin(8*x) - 32*x*(sin(8*x)^2*(3 - 64*x^2) + 64*x^2*cos(8*x)^2 + 48*x*cos(8*x)*sin(8*x))*cos(8*x) + 192*x^2*cos(8*x)^2*(3*sin(8*x) + 16*x*cos(8*x)) + 48*x*(3*sin(8*x) + 16*x*cos(8*x))*cos(8*x)*sin(8*x)) - 12*(3*sin(8*x) + 16*x*cos(8*x))*(sin(8*x)^2*(3 - 64*x^2) + 64*x^2*cos(8*x)^2 + 48*x*cos(8*x)*sin(8*x))*log(x^3*sin(8*x)^2) + 18*(3*sin(8*x) + 16*x*cos(8*x))^2*log(x^3*sin(8*x)^2)*sin(8*x) + 96*x*(3*sin(8*x) + 16*x*cos(8*x))^2*cos(8*x)*log(x^3*sin(8*x)^2))/(8*x^3*log(x^3*sin(8*x)^2)^(5/2)*sin(8*x)^3)
Potencias
[src]
/ 2 / 2 2 \ / 2 2 \ / 2 \ 3 2 / 2 2 \ 2\
| / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ / / -8*I*x 8*I*x\ / -8*I*x 8*I*x\\ | / -8*I*x 8*I*x\ 2 / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ | | / -8*I*x 8*I*x\ 2 / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ | / -8*I*x 8*I*x\ | 2 2 / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ | / / -8*I*x 8*I*x\ / -8*I*x 8*I*x\\ / / -8*I*x 8*I*x\ / -8*I*x 8*I*x\\ / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ / / -8*I*x 8*I*x\\ / / -8*I*x 8*I*x\ / -8*I*x 8*I*x\\ | / -8*I*x 8*I*x\ 2 / -8*I*x 8*I*x\ / -8*I*x 8*I*x\ | / / -8*I*x 8*I*x\ / -8*I*x 8*I*x\\ |
| / -8*I*x 8*I*x\ |e e | |e e | | |e e | 3*I*\- e + e /| | 9*\- e + e / 2 / -8*I*x 8*I*x\ 2 |e e | |e e | / -8*I*x 8*I*x\| | 3*\- e + e / 2 / -8*I*x 8*I*x\ 2 |e e | |e e | / -8*I*x 8*I*x\ 3 |e e | / -8*I*x 8*I*x\| |e e | | / -8*I*x 8*I*x\ 2 / -8*I*x 8*I*x\ 2 |e e | |e e | / -8*I*x 8*I*x\| | |e e | 3*I*\- e + e /| | |e e | 3*I*\- e + e /| |e e | |e e | | / -8*I*x 8*I*x\ |e e || | |e e | 9*I*\- e + e /| | 3*\- e + e / 2 / -8*I*x 8*I*x\ 2 |e e | |e e | / -8*I*x 8*I*x\| | |e e | 3*I*\- e + e /| |
|- 9*I*\- e + e / + 96*x*|------- + ------| / -8*I*x 8*I*x\ 768*|------- + ------| *|16*x*|------- + ------| - ------------------------| 2*I*|- ----------------------- + 96*x *\- e + e / + 384*x *|------- + ------| - 144*I*x*|------- + ------|*\- e + e /| 2*I*|- ----------------------- + 144*x *\- e + e / + 576*x *|------- + ------| - 72*I*x*|------- + ------|*\- e + e / + 1024*I*x *|------- + ------|*\- e + e /| 4*|------- + ------|*|- 24*\- e + e / + 512*x *\- e + e / + 2048*x *|------- + ------| - 768*I*x*|------- + ------|*\- e + e /| 3*|16*x*|------- + ------| - ------------------------| 48*|16*x*|------- + ------| - ------------------------| *|------- + ------| 2*I*|------- + ------|*|- 72*I*\- e + e / + 768*x*|------- + ------|| 2*|48*x*|------- + ------| - ------------------------|*|- ----------------------- + 16*x *\- e + e / + 64*x *|------- + ------| - 24*I*x*|------- + ------|*\- e + e /| 9*I*|16*x*|------- + ------| - ------------------------| |
___ | \ 2 2 / / -8*I*x 8*I*x\ |e e | \ 2 2 / \ \ 2 2 / 2 / \ 2 \ 2 2 / \ 2 2 / / \ 4 \ 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 / \ 4 \ 2 2 / \ 2 2 / / \ \ 2 2 / 2 / |
2*I*\/ 3 *|---------------------------------------------------- - 96*I*\- e + e / + 1024*x*|------- + ------| - ---------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------- - --------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------|
| 2 \ 2 2 / 2 2 / -8*I*x 8*I*x\ 2 / -8*I*x 8*I*x\ 2 / 2 \ / 2 \ / -8*I*x 8*I*x\ / 2 \ / 2 \|
| x / -8*I*x 8*I*x\ x *\- e + e / x *\- e + e / / -8*I*x 8*I*x\ 2 | 3 / -8*I*x 8*I*x\ | 2 | 3 / -8*I*x 8*I*x\ | x*\- e + e / 2 | 3 / -8*I*x 8*I*x\ | | 3 / -8*I*x 8*I*x\ ||
| \- e + e / x*\- e + e / 2 / -8*I*x 8*I*x\ 2|-x *\- e + e / | / -8*I*x 8*I*x\ |-x *\- e + e / | 2 / -8*I*x 8*I*x\ |-x *\- e + e / | 2 / -8*I*x 8*I*x\ |-x *\- e + e / ||
| 2*x *\- e + e / *log |--------------------------| x*\- e + e / *log|--------------------------| x *\- e + e / *log|--------------------------| 2*x *\- e + e /*log|--------------------------||
\ \ 4 / \ 4 / \ 4 / \ 4 //
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/ / 2 \
/ | 3 / -8*I*x 8*I*x\ |
/ -8*I*x 8*I*x\ / |-x *\- e + e / |
x*\- e + e /* / log|--------------------------|
\/ \ 4 /
$$\frac{2 \sqrt{3} i \left(1024 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - \frac{768 \left(16 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - \frac{3 i \left(e^{8 i x} - e^{- 8 i x}\right)}{2}\right) \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)^{2}}{\left(e^{8 i x} - e^{- 8 i x}\right)^{2}} - 96 i \left(e^{8 i x} - e^{- 8 i x}\right) - \frac{48 \left(16 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - \frac{3 i \left(e^{8 i x} - e^{- 8 i x}\right)}{2}\right)^{2} \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)}{x \left(e^{8 i x} - e^{- 8 i x}\right)^{2} \log{\left(- \frac{x^{3} \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4} \right)}} + \frac{2 i \left(768 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - 72 i \left(e^{8 i x} - e^{- 8 i x}\right)\right) \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)}{x \left(e^{8 i x} - e^{- 8 i x}\right)} + \frac{4 \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) \left(2048 x^{2} \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)^{2} + 512 x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)^{2} - 768 i x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) \left(e^{8 i x} - e^{- 8 i x}\right) - 24 \left(e^{8 i x} - e^{- 8 i x}\right)^{2}\right)}{x \left(e^{8 i x} - e^{- 8 i x}\right)^{2}} - \frac{3 \left(16 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - \frac{3 i \left(e^{8 i x} - e^{- 8 i x}\right)}{2}\right)^{3}}{2 x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)^{2} \log{\left(- \frac{x^{3} \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4} \right)}^{2}} + \frac{9 i \left(16 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - \frac{3 i \left(e^{8 i x} - e^{- 8 i x}\right)}{2}\right)^{2}}{2 x^{2} \left(e^{8 i x} - e^{- 8 i x}\right) \log{\left(- \frac{x^{3} \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4} \right)}} + \frac{2 \left(48 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - \frac{9 i \left(e^{8 i x} - e^{- 8 i x}\right)}{2}\right) \left(64 x^{2} \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)^{2} + 16 x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)^{2} - 24 i x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) \left(e^{8 i x} - e^{- 8 i x}\right) - \frac{3 \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4}\right)}{x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)^{2} \log{\left(- \frac{x^{3} \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4} \right)}} + \frac{96 x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) - 9 i \left(e^{8 i x} - e^{- 8 i x}\right)}{x^{2}} - \frac{2 i \left(384 x^{2} \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)^{2} + 96 x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)^{2} - 144 i x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) \left(e^{8 i x} - e^{- 8 i x}\right) - \frac{9 \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{2}\right)}{x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)} + \frac{2 i \left(1024 i x^{3} \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) \left(e^{8 i x} - e^{- 8 i x}\right) + 576 x^{2} \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right)^{2} + 144 x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)^{2} - 72 i x \left(\frac{e^{8 i x}}{2} + \frac{e^{- 8 i x}}{2}\right) \left(e^{8 i x} - e^{- 8 i x}\right) - \frac{3 \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4}\right)}{x^{2} \left(e^{8 i x} - e^{- 8 i x}\right)}\right)}{x \left(e^{8 i x} - e^{- 8 i x}\right) \sqrt{\log{\left(- \frac{x^{3} \left(e^{8 i x} - e^{- 8 i x}\right)^{2}}{4} \right)}}}$$
/ 2 2 2 2 2 3 2 2 2 2 2 2 / 2 2 2 2 2 \ 3 2 2 / 2 2 2 2 2 \\
___ | 18*sin(8*x) + 96*x*cos(8*x) 3*sin (8*x) - 576*x *sin (8*x) + 576*x *cos (8*x) - 2048*x *cos(8*x)*sin(8*x) + 144*x*cos(8*x)*sin(8*x) 18*sin (8*x) - 384*x *sin (8*x) + 384*x *cos (8*x) + 288*x*cos(8*x)*sin(8*x) 192*cos (8*x)*(3*sin(8*x) + 16*x*cos(8*x)) (144*sin(8*x) + 768*x*cos(8*x))*cos(8*x) \96*sin (8*x) - 2048*x *sin (8*x) + 2048*x *cos (8*x) + 1536*x*cos(8*x)*sin(8*x)/*cos(8*x) 3*(3*sin(8*x) + 16*x*cos(8*x)) 9*(3*sin(8*x) + 16*x*cos(8*x)) 12*(3*sin(8*x) + 16*x*cos(8*x)) *cos(8*x) (9*sin(8*x) + 48*x*cos(8*x))*\3*sin (8*x) - 64*x *sin (8*x) + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/|
\/ 3 *|192*sin(8*x) + --------------------------- + 1024*x*cos(8*x) + ------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------- + ------------------------------------------ + ---------------------------------------- - ------------------------------------------------------------------------------------------ + --------------------------------- + ------------------------------- + ----------------------------------------- - -------------------------------------------------------------------------------------------------------|
| 2 2 2 2 x*sin(8*x) 2 2 2/ 3 2 \ 2 2 / 3 2 \ / 3 2 \ 2 2 / 3 2 \ 2 |
\ x x *sin(8*x) x *sin(8*x) sin (8*x) x*sin (8*x) 8*x *log \x *sin (8*x)/*sin (8*x) 4*x *log\x *sin (8*x)/*sin(8*x) x*log\x *sin (8*x)/*sin (8*x) 2*x *log\x *sin (8*x)/*sin (8*x) /
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/ / 3 2 \
x*\/ log\x *sin (8*x)/ *sin(8*x)
$$\frac{\sqrt{3} \left(1024 x \cos{\left(8 x \right)} + \frac{192 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \cos^{2}{\left(8 x \right)}}{\sin^{2}{\left(8 x \right)}} + 192 \sin{\left(8 x \right)} + \frac{12 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2} \cos{\left(8 x \right)}}{x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}} + \frac{\left(768 x \cos{\left(8 x \right)} + 144 \sin{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin{\left(8 x \right)}} - \frac{\left(- 2048 x^{2} \sin^{2}{\left(8 x \right)} + 2048 x^{2} \cos^{2}{\left(8 x \right)} + 1536 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 96 \sin^{2}{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin^{2}{\left(8 x \right)}} + \frac{3 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{3}}{8 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)}} + \frac{9 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2}}{4 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)}} - \frac{\left(48 x \cos{\left(8 x \right)} + 9 \sin{\left(8 x \right)}\right) \left(- 64 x^{2} \sin^{2}{\left(8 x \right)} + 64 x^{2} \cos^{2}{\left(8 x \right)} + 48 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)}{2 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}} + \frac{96 x \cos{\left(8 x \right)} + 18 \sin{\left(8 x \right)}}{x^{2}} - \frac{- 384 x^{2} \sin^{2}{\left(8 x \right)} + 384 x^{2} \cos^{2}{\left(8 x \right)} + 288 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 18 \sin^{2}{\left(8 x \right)}}{x^{2} \sin{\left(8 x \right)}} + \frac{- 2048 x^{3} \sin{\left(8 x \right)} \cos{\left(8 x \right)} - 576 x^{2} \sin^{2}{\left(8 x \right)} + 576 x^{2} \cos^{2}{\left(8 x \right)} + 144 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}}{x^{2} \sin{\left(8 x \right)}}\right)}{x \sqrt{\log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}} \sin{\left(8 x \right)}}$$
/ 2 2 2 2 2 2 2 2 2 2 3 2 / 2 2 2 2 2 \ 3 2 2 / 2 2 2 2 2 \\
___ | 18*sin(8*x) + 96*x*cos(8*x) - 18*sin (8*x) - 384*x *cos (8*x) + 384*x *sin (8*x) - 288*x*cos(8*x)*sin(8*x) 3*sin (8*x) - 576*x *sin (8*x) + 576*x *cos (8*x) - 2048*x *cos(8*x)*sin(8*x) + 144*x*cos(8*x)*sin(8*x) cos (8*x)*(576*sin(8*x) + 3072*x*cos(8*x)) (144*sin(8*x) + 768*x*cos(8*x))*cos(8*x) \96*sin (8*x) - 2048*x *sin (8*x) + 2048*x *cos (8*x) + 1536*x*cos(8*x)*sin(8*x)/*cos(8*x) 3*(3*sin(8*x) + 16*x*cos(8*x)) 9*(3*sin(8*x) + 16*x*cos(8*x)) 12*(3*sin(8*x) + 16*x*cos(8*x)) *cos(8*x) (9*sin(8*x) + 48*x*cos(8*x))*\3*sin (8*x) - 64*x *sin (8*x) + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/|
\/ 3 *|192*sin(8*x) + --------------------------- + 1024*x*cos(8*x) + ------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------- + ------------------------------------------ + ---------------------------------------- - ------------------------------------------------------------------------------------------ + --------------------------------- + ------------------------------- + ----------------------------------------- - -------------------------------------------------------------------------------------------------------|
| 2 2 2 2 x*sin(8*x) 2 2 2/ 3 2 \ 2 2 / 3 2 \ / 3 2 \ 2 2 / 3 2 \ 2 |
\ x x *sin(8*x) x *sin(8*x) sin (8*x) x*sin (8*x) 8*x *log \x *sin (8*x)/*sin (8*x) 4*x *log\x *sin (8*x)/*sin(8*x) x*log\x *sin (8*x)/*sin (8*x) 2*x *log\x *sin (8*x)/*sin (8*x) /
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___________________
/ / 3 2 \
x*\/ log\x *sin (8*x)/ *sin(8*x)
$$\frac{\sqrt{3} \left(1024 x \cos{\left(8 x \right)} + \frac{\left(3072 x \cos{\left(8 x \right)} + 576 \sin{\left(8 x \right)}\right) \cos^{2}{\left(8 x \right)}}{\sin^{2}{\left(8 x \right)}} + 192 \sin{\left(8 x \right)} + \frac{12 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2} \cos{\left(8 x \right)}}{x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}} + \frac{\left(768 x \cos{\left(8 x \right)} + 144 \sin{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin{\left(8 x \right)}} - \frac{\left(- 2048 x^{2} \sin^{2}{\left(8 x \right)} + 2048 x^{2} \cos^{2}{\left(8 x \right)} + 1536 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 96 \sin^{2}{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin^{2}{\left(8 x \right)}} + \frac{3 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{3}}{8 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)}} + \frac{9 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2}}{4 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)}} - \frac{\left(48 x \cos{\left(8 x \right)} + 9 \sin{\left(8 x \right)}\right) \left(- 64 x^{2} \sin^{2}{\left(8 x \right)} + 64 x^{2} \cos^{2}{\left(8 x \right)} + 48 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)}{2 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}} + \frac{96 x \cos{\left(8 x \right)} + 18 \sin{\left(8 x \right)}}{x^{2}} + \frac{384 x^{2} \sin^{2}{\left(8 x \right)} - 384 x^{2} \cos^{2}{\left(8 x \right)} - 288 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} - 18 \sin^{2}{\left(8 x \right)}}{x^{2} \sin{\left(8 x \right)}} + \frac{- 2048 x^{3} \sin{\left(8 x \right)} \cos{\left(8 x \right)} - 576 x^{2} \sin^{2}{\left(8 x \right)} + 576 x^{2} \cos^{2}{\left(8 x \right)} + 144 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}}{x^{2} \sin{\left(8 x \right)}}\right)}{x \sqrt{\log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}} \sin{\left(8 x \right)}}$$
sqrt(3)*(192*sin(8*x) + (18*sin(8*x) + 96*x*cos(8*x))/x^2 + 1024*x*cos(8*x) + (-18*sin(8*x)^2 - 384*x^2*cos(8*x)^2 + 384*x^2*sin(8*x)^2 - 288*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) + (3*sin(8*x)^2 - 576*x^2*sin(8*x)^2 + 576*x^2*cos(8*x)^2 - 2048*x^3*cos(8*x)*sin(8*x) + 144*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) + cos(8*x)^2*(576*sin(8*x) + 3072*x*cos(8*x))/sin(8*x)^2 + (144*sin(8*x) + 768*x*cos(8*x))*cos(8*x)/(x*sin(8*x)) - (96*sin(8*x)^2 - 2048*x^2*sin(8*x)^2 + 2048*x^2*cos(8*x)^2 + 1536*x*cos(8*x)*sin(8*x))*cos(8*x)/(x*sin(8*x)^2) + 3*(3*sin(8*x) + 16*x*cos(8*x))^3/(8*x^2*log(x^3*sin(8*x)^2)^2*sin(8*x)^2) + 9*(3*sin(8*x) + 16*x*cos(8*x))^2/(4*x^2*log(x^3*sin(8*x)^2)*sin(8*x)) + 12*(3*sin(8*x) + 16*x*cos(8*x))^2*cos(8*x)/(x*log(x^3*sin(8*x)^2)*sin(8*x)^2) - (9*sin(8*x) + 48*x*cos(8*x))*(3*sin(8*x)^2 - 64*x^2*sin(8*x)^2 + 64*x^2*cos(8*x)^2 + 48*x*cos(8*x)*sin(8*x))/(2*x^2*log(x^3*sin(8*x)^2)*sin(8*x)^2))/(x*sqrt(log(x^3*sin(8*x)^2))*sin(8*x))
Compilar la expresión
[src]
/ 2 2 2 2 2 3 2 2 2 2 2 2 / 2 2 2 2 2 \ 3 2 2 / 2 2 2 2 2 \\
___ | 18*sin(8*x) + 96*x*cos(8*x) 3*sin (8*x) - 576*x *sin (8*x) + 576*x *cos (8*x) - 2048*x *cos(8*x)*sin(8*x) + 144*x*cos(8*x)*sin(8*x) 18*sin (8*x) - 384*x *sin (8*x) + 384*x *cos (8*x) + 288*x*cos(8*x)*sin(8*x) 192*cos (8*x)*(3*sin(8*x) + 16*x*cos(8*x)) (144*sin(8*x) + 768*x*cos(8*x))*cos(8*x) \96*sin (8*x) - 2048*x *sin (8*x) + 2048*x *cos (8*x) + 1536*x*cos(8*x)*sin(8*x)/*cos(8*x) 3*(3*sin(8*x) + 16*x*cos(8*x)) 9*(3*sin(8*x) + 16*x*cos(8*x)) 12*(3*sin(8*x) + 16*x*cos(8*x)) *cos(8*x) (9*sin(8*x) + 48*x*cos(8*x))*\3*sin (8*x) - 64*x *sin (8*x) + 64*x *cos (8*x) + 48*x*cos(8*x)*sin(8*x)/|
\/ 3 *|192*sin(8*x) + --------------------------- + 1024*x*cos(8*x) + ------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------- + ------------------------------------------ + ---------------------------------------- - ------------------------------------------------------------------------------------------ + --------------------------------- + ------------------------------- + ----------------------------------------- - -------------------------------------------------------------------------------------------------------|
| 2 2 2 2 x*sin(8*x) 2 2 2/ 3 2 \ 2 2 / 3 2 \ / 3 2 \ 2 2 / 3 2 \ 2 |
\ x x *sin(8*x) x *sin(8*x) sin (8*x) x*sin (8*x) 8*x *log \x *sin (8*x)/*sin (8*x) 4*x *log\x *sin (8*x)/*sin(8*x) x*log\x *sin (8*x)/*sin (8*x) 2*x *log\x *sin (8*x)/*sin (8*x) /
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___________________
/ / 3 2 \
x*\/ log\x *sin (8*x)/ *sin(8*x)
$$\frac{\sqrt{3} \left(1024 x \cos{\left(8 x \right)} + \frac{192 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right) \cos^{2}{\left(8 x \right)}}{\sin^{2}{\left(8 x \right)}} + 192 \sin{\left(8 x \right)} + \frac{12 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2} \cos{\left(8 x \right)}}{x \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}} + \frac{\left(768 x \cos{\left(8 x \right)} + 144 \sin{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin{\left(8 x \right)}} - \frac{\left(- 2048 x^{2} \sin^{2}{\left(8 x \right)} + 2048 x^{2} \cos^{2}{\left(8 x \right)} + 1536 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 96 \sin^{2}{\left(8 x \right)}\right) \cos{\left(8 x \right)}}{x \sin^{2}{\left(8 x \right)}} + \frac{3 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{3}}{8 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}^{2} \sin^{2}{\left(8 x \right)}} + \frac{9 \left(16 x \cos{\left(8 x \right)} + 3 \sin{\left(8 x \right)}\right)^{2}}{4 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin{\left(8 x \right)}} - \frac{\left(48 x \cos{\left(8 x \right)} + 9 \sin{\left(8 x \right)}\right) \left(- 64 x^{2} \sin^{2}{\left(8 x \right)} + 64 x^{2} \cos^{2}{\left(8 x \right)} + 48 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}\right)}{2 x^{2} \log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)} \sin^{2}{\left(8 x \right)}} + \frac{96 x \cos{\left(8 x \right)} + 18 \sin{\left(8 x \right)}}{x^{2}} - \frac{- 384 x^{2} \sin^{2}{\left(8 x \right)} + 384 x^{2} \cos^{2}{\left(8 x \right)} + 288 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 18 \sin^{2}{\left(8 x \right)}}{x^{2} \sin{\left(8 x \right)}} + \frac{- 2048 x^{3} \sin{\left(8 x \right)} \cos{\left(8 x \right)} - 576 x^{2} \sin^{2}{\left(8 x \right)} + 576 x^{2} \cos^{2}{\left(8 x \right)} + 144 x \sin{\left(8 x \right)} \cos{\left(8 x \right)} + 3 \sin^{2}{\left(8 x \right)}}{x^{2} \sin{\left(8 x \right)}}\right)}{x \sqrt{\log{\left(x^{3} \sin^{2}{\left(8 x \right)} \right)}} \sin{\left(8 x \right)}}$$
sqrt(3)*(192*sin(8*x) + (18*sin(8*x) + 96*x*cos(8*x))/x^2 + 1024*x*cos(8*x) + (3*sin(8*x)^2 - 576*x^2*sin(8*x)^2 + 576*x^2*cos(8*x)^2 - 2048*x^3*cos(8*x)*sin(8*x) + 144*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) - (18*sin(8*x)^2 - 384*x^2*sin(8*x)^2 + 384*x^2*cos(8*x)^2 + 288*x*cos(8*x)*sin(8*x))/(x^2*sin(8*x)) + 192*cos(8*x)^2*(3*sin(8*x) + 16*x*cos(8*x))/sin(8*x)^2 + (144*sin(8*x) + 768*x*cos(8*x))*cos(8*x)/(x*sin(8*x)) - (96*sin(8*x)^2 - 2048*x^2*sin(8*x)^2 + 2048*x^2*cos(8*x)^2 + 1536*x*cos(8*x)*sin(8*x))*cos(8*x)/(x*sin(8*x)^2) + 3*(3*sin(8*x) + 16*x*cos(8*x))^3/(8*x^2*log(x^3*sin(8*x)^2)^2*sin(8*x)^2) + 9*(3*sin(8*x) + 16*x*cos(8*x))^2/(4*x^2*log(x^3*sin(8*x)^2)*sin(8*x)) + 12*(3*sin(8*x) + 16*x*cos(8*x))^2*cos(8*x)/(x*log(x^3*sin(8*x)^2)*sin(8*x)^2) - (9*sin(8*x) + 48*x*cos(8*x))*(3*sin(8*x)^2 - 64*x^2*sin(8*x)^2 + 64*x^2*cos(8*x)^2 + 48*x*cos(8*x)*sin(8*x))/(2*x^2*log(x^3*sin(8*x)^2)*sin(8*x)^2))/(x*sqrt(log(x^3*sin(8*x)^2))*sin(8*x))