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anonymous
 3 years ago
find the integral of cot^3xcsc^3xdx
anonymous
 3 years ago
find the integral of cot^3xcsc^3xdx

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anonymous
 3 years 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you want integral of cot^3(x)*csc^3(x) dx right?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sorry about that should have made it more clear

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Take 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so it's just a simple substitution
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