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d(2x)/sin2x的不定积分是什么?
题目详情
d(2x)/sin2x的不定积分是什么?
▼优质解答
答案和解析
=sin2xd2x/(sin^2 2x)
=-dcos2x/(1-cos^2 2x)
=-1/2dcos2x/(1-cos2x)-1/2dcos2x/(1+cos2x)
=1/2dln(1-cos2x)-1/2dln(1+cos2x)
=1/2dln[(1-cos2x)/(1+cos2x)]
=dlntanx
or
=dx/sinxcosx
=sec^xdx/tanx
=dtanx/tanx
=dlntanx
=-dcos2x/(1-cos^2 2x)
=-1/2dcos2x/(1-cos2x)-1/2dcos2x/(1+cos2x)
=1/2dln(1-cos2x)-1/2dln(1+cos2x)
=1/2dln[(1-cos2x)/(1+cos2x)]
=dlntanx
or
=dx/sinxcosx
=sec^xdx/tanx
=dtanx/tanx
=dlntanx
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