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求1/sin2x的定积分
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求1/sin2x的定积分
▼优质解答
答案和解析
∫dx/sin2x
=∫(sin^2 x +cos^2 x)dx/2sinxcosx
=1/2∫sinxdx/cosx +1/2∫cosxdx/sinx
=-1/2∫dcosx/cosx +1/2∫dsinx/sinx
=-1/2lncosx +1/2lnsinx +C
=1/2ln(sinx/cosx)+C
=ln√(sinx/cosx) +C
=∫(sin^2 x +cos^2 x)dx/2sinxcosx
=1/2∫sinxdx/cosx +1/2∫cosxdx/sinx
=-1/2∫dcosx/cosx +1/2∫dsinx/sinx
=-1/2lncosx +1/2lnsinx +C
=1/2ln(sinx/cosx)+C
=ln√(sinx/cosx) +C
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