xcosx/(sinx)^3 dx
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xcosx/(sinx)^3dxxcosx/(sinx)^3dxxcosx/(sinx)^3dx求不定积分∫[(xcosx)/(sin³x)]dx原式=∫xcotxcsc²xdx=
xcosx/(sinx)^3 dx
xcosx/(sinx)^3 dx
xcosx/(sinx)^3 dx
求不定积分∫[(xcosx)/(sin³x)]dx
原式=∫xcotxcsc²xdx=-∫xcotxd(cotx)=-(1/2)∫xd(cot²x)=-(1/2)[xcot²x-∫cot²xdx]
=-(1/2)[xcot²x-∫(csc²x-1)dx]=-(1/2)[xcot²x+cotx+x]+C=-(1/2)[(1+cot²x)x+cotx]+C
=-(1/2)(xcsc²x+cotx)+C
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