Hint

[잡념이]

Hint

"int" = "integration"

int cosec^3(x) dx
= int cosec(x){1+cot^2(x)} dx
= int cosec(x) dx + int cosec(x)cot^2(x) dx

int cosec(x) dx
= int cosec(x)*{cosec(x) + cot(x)}/{cosec(x) + cot(x)} dx
= int {cosex^2(x) + cosec(x)cot(x)}/{cot(x) + cosec(x)} dx
= ln (cot(x) + cosec(x)) + C

int cosec(x)cot^2(x) dx
= int cosec(x)cot(x)cot(x) dx
= cosec(x)cot(x) + D - int cosec(x)cosec^2(x) dx
= cosec(x)cot(x) + D - int cosex^3(x) dx

Then,
int cosec^3(x) dx
= ln (cot(x) + cosec(x)) + cosec(x)cot(x) + E - int cosec^3(x) dx