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Answer 1 · 2015-12-07T15:46:53

#int1/sin^2(x)*cos^3(x)/sin^3(x)*cos^2(x)/sin^2(x)#

#t = cot^3(x)#

#dt = -3cot^2(t)csc^2(x)#

#-1/3int-3csc^2(x)cot^2(x)cot^3(x)dx#

this become :

#-1/3intt^2dt#

#-1/6[t^2]+C#

Substitute back

#-1/6cot^6(x)#