recall your half-angle formulas for hyperbolic functions:
sinh(x/2) = √((coshx-1)/2)
so,
√(coshx-1) = √2sinh(x/2)
dx/√(coshx-1) = 1/√2 csch(x/2) dx
now just use your standard form for integrating csch(u)
integrate dx/root(coshx-1)
plz show step
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