怎么用微积分计算积分上下限

Question

如题所述

Answer 1

∫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