csc u du


csc u du  =

csc u * csc u + cot u   du  =
    csc u + cot u

     csc2 u + cot2  du =
cot u + csc u

--csc2 u - cot2 u du =
cot u + csc u

- ln|cot u + csc u|  +  C


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