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9Â¥: Originally posted by shizheng0124 at 2014-04-04 13:26:01
\int {\frac{{{{\sin }^4}\left( x \right) + {{\cos }^4}\left( x \right)}}{{1 + 4\sin \left( x \right)cos\left( x \right)}}dx}
= \int {\frac{{{{\sin }^4}\left( x \right) + {{\cos }^4}\left( x \right) ...

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2Â¥2014-04-04 07:44:48
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3Â¥2014-04-04 08:45:22
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Áîu=tg(x/2),x=2*Arctgu ,
dx=2*du/(1+u^2),
Sinx=2*tg(x/2)*Cos^2(x/2)=2*u/(1+u^2),
Cosx=1-2*Sin^2(x/2)=1-2*tg^2(x/2)*Cos^2(x/2)=(1-u^2)/(1+u^2)
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