`int sinh(1-2x) dx` Find the indefinite integral

It is known that `(cosh)' = sinhx,` so `int sinhx dx = coshx + C.` To reduce the given integral to the known one, make the substitution `u = 1 - 2x.` Then `du = -2 dx,` `dx = -1/2 du,` and the integral becomes

`int sinh(u)*(-1/2) du = -1/2 int sinh(u) du =`

`= -1/2 cosh(u) + C = -1/2 cosh(1 - 2x) + C,`

where `C` is an arbitrary constant.