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sat_chen Group TitleBest ResponseYou've already chosen the best response.0
i got csc^5x/5 + csc^3x/3 + C can someone pls tell me if im doing it right pls let me know thanks
 one year ago

mivanov Group TitleBest ResponseYou've already chosen the best response.1
you want integral of cot^3(x)*csc^3(x) dx right?
 one year ago

escolas Group TitleBest ResponseYou've already chosen the best response.0
is this (cotx)^3*(cscx)^3 dx?
 one year ago

sat_chen Group TitleBest ResponseYou've already chosen the best response.0
sorry about that should have made it more clear
 one year ago

mivanov Group TitleBest ResponseYou've already chosen the best response.1
Take the integral: integral cot^3(x) csc^3(x) dx For the integrand cot^3(x) csc^3(x), use the trigonometric identity cot^2(x) = csc^2(x)1: = integral cot(x) csc^3(x) (csc^2(x)1) dx For the integrand cot(x) csc^3(x) (csc^2(x)1), substitute u = csc(x) and du = (cot(x) csc(x)) dx: =  integral u^2 (u^21) du Expanding the integrand u^2 (u^21) gives u^4u^2: =  integral (u^4u^2) du Integrate the sum term by term and factor out constants: = integral u^2 du integral u^4 du The integral of u^4 is u^5/5: = integral u^2 duu^5/5 The integral of u^2 is u^3/3: = u^3/3u^5/5+constant Substitute back for u = csc(x): = (csc^3(x))/3(csc^5(x))/5+constant Which is equal to: Answer:   = 1/30 ((5 cos(2 x)+1) csc^5(x))+constant
 one year ago

mivanov Group TitleBest ResponseYou've already chosen the best response.1
so it's just a simple substitution
 one year ago
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