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Question Number 140988 by mohammad17 last updated on 14/May/21

∫((−csc^2 x)/((cscx+cotx)^3 ))dx

∫−csc2x(cscx+cotx)3dx

Answered by MJS_new last updated on 14/May/21

∫((−csc^2 x)/((csc x +cot x)))dx= [t=cos x → dx=−(dt/(sin x))] =∫(dt/((t+1)^3 ))=−(1/(2(t+1)^2 ))=−(1/(2(1+cos x)^2 ))+C

∫−csc2x(cscx+cotx)dx=[t=cosx→dx=−dtsinx]=∫dt(t+1)3=−12(t+1)2=−12(1+cosx)2+C

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