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Calculus

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integral of cscx^(2/3)(cot^3)x
i know that cot^2x is csc^2(x)-1, but i just don't understand how to solve the cscx^(2/3), any help? i also know that its trig integrals/substitution...

  • Calculus - ,

    let u = csc(x)
    du = -csc(x) cot(x)

    cot^2 = csc^2 - 1

    and you have

    csc^(2/3) (csc^2-1)cot(x)
    = csc^(5/3)(csc*cot) - csc^(-1/3)(csc*cot)
    = [-u^5/3 + u^(-1/3)] du

    all downhill from there

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