∫cos2x/(sinx^2*cosx^2)dx求积分

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∫cos2x/(sinx^2*cosx^2)dx求积分∫cos2x/(sinx^2*cosx^2)dx求积分∫cos2x/(sinx^2*cosx^2)dx求积分∫cos2x/(sinx^2*cosx

∫cos2x/(sinx^2*cosx^2)dx求积分
∫cos2x/(sinx^2*cosx^2)dx求积分

∫cos2x/(sinx^2*cosx^2)dx求积分
∫cos2x/(sinx^2*cosx^2)dx=∫[(cosx)^2-(sin)^2]/(sinx^2*cosx^2)dx=∫1/(sinx)^2-1/(cosx)^2dx=-cotx-tanx+c


原式=4∫cos2x/(sin²2x)dx
=2∫dsin(2x)/(sin²(2x))
=2∫(sin(2x))^(-2)dsin(2x)
=-2/sin2x+C

∫cos2x/(sinx^2*cosx^2)dx=∫(1/sinx^2-1/cosx^2dx=∫(cscx^2-scsx^2)dx= -cotx-tanx