∫ x/(sinx)^2dx
=-∫ xd(cosx/sinx)
=-xcosx/sinx+∫ cosx/sinxdx
=-xcosx/sinx+∫1/sinxd(sinx)
=-xcosx/sinx+lnsinx
(π/4,π/3)代入结果为
1/36(9-4√3)π+1/2ln3/2
∫ x/(sinx)^2dx
=-∫ xd(cosx/sinx)
=-xcosx/sinx+∫ cosx/sinxdx
=-xcosx/sinx+∫1/sinxd(sinx)
=-xcosx/sinx+lnsinx
(π/4,π/3)代入结果为
1/36(9-4√3)π+1/2ln3/2