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

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

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

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

mivanov
 one year ago
Best ResponseYou've already chosen the best response.1Take 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

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