Question

∫sin(lnx)dx

Answer 1

by parts :)

Answer 2

let u = ln(x) then e^u=x du e^u = dx int(sin(u)e^udu is integrable by parts

Answer 3

∫udv = uv - ∫vdu
Take u = sin(lnx) and v=x here. Do integration by part twice.