integrate dx/root(coshx-1)

Question

plz show step

Answer 1

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)