1、∫sin(3π/2-α)dα
=-∫sin(3π/2-α)d(3π/2-α)
=cos(3π/2-α)+c
=-cos(π/2-α)+c
=-sinα+c
2、图例解析如下：
1、∫sin(3π/2-α)dα
=-∫sin(3π/2-α)d(3π/2-α)
=cos(3π/2-α)+c
=-cos(π/2-α)+c
=-sinα+c
2、图例解析如下：
1、∫cos(3π/2-α)dα
=-∫cos(3π/2-α)d(3π/2-α)
=-sin(3π/2-α)+c
=sin(π/2-α)+c
=cosα+c
2、图例解析如下：
1、∫tan(3π/2-α)dα
=-∫[sin(3π/2-α) d(3π/2-α)/ cos(3π/2-α)]
=∫d cos(3π/2-α)/cos(3π/2-α)
=ln|cos(3π/2-α)|+c
=ln|sinα|+c
2、图例解析如下：
1、∫cot(3π/2-α)dα
=-∫[cos(3π/2-α) d(3π/2-α)/ sin(3π/2-α)]
=-∫d sin(3π/2-α)/sin(3π/2-α)
=-ln|sin(3π/2-α)|+c
=-ln|cosα|+c
2、图例解析如下：
1、∫sec(3π/2-α)dα
=-∫d(3π/2-α)/ cos(3π/2-α)
=-∫cos(3π/2-α)d(3π/2-α)/ [cos(3π/2-α)]^2
=-∫dsin(3π/2-α)/ {1-[sin(3π/2-α)]^2}
=-∫dsin(3π/2-α)/ {[1-sin(3π/2-α)][1+ sin(3π/2-α)]}
=-(1/2){∫dsin(3π/2-α)/ [1-sin(3π/2-α)]+∫dsin(3π/2-α)/ [1+sin(3π/2-α)]}
=-(1/2)ln{[1+sin(3π/2-α)]/ [1-sin(3π/2-α)]}+c
=-(1/2)ln[(1-cosα)/(1+cosα)]+c
=-(1/2)ln[(1-cosα)^2/(sinα)^2]+c
=-ln|(1-cosα)/sinα|+c
=-ln|cscα-cotα|+c
2、图例解析如下：
1、∫csc(3π/2-α)dα
=-∫d(3π/2-α)/ sin(3π/2-α)
=-∫sin(3π/2-α)d(3π/2-α)/ [sin(3π/2-α)]^2
=∫dcos(3π/2-α)/ {1-[cos(3π/2-α)]^2}
=∫dcos(3π/2-α)/ {[1-cos(3π/2-α)][1+ cos(3π/2-α)]}
=(1/2){∫dcos(3π/2-α)/ [1-cos(3π/2-α)]+∫dcos(3π/2-α)/ [1+cos(3π/2-α)]}
=(1/2)ln{[1+cos(3π/2-α)]/ [1-cos(3π/2-α)]}+c
=(1/2)ln[(1+sinα)/(1-sinα)]+c
=(1/2)ln[(1+sinα)^2/(cosα)^2]+c
=ln|(1+sinα)/cosα|+c
=ln|secα+tana|+c
2、图例解析如下：
