What is y if dy/dx=sin(lnx)/x?

To determine the primitive y, we'll have to calculate the
indefinite integral of dy.

We'll solve by replacing ln x by
t:

ln x = t

We'll
differentiate both sides:

dx/x =
dt

We'll re-write the integral in the new variable
t:

Int dy = Int sin(lnx)
dx/x

Int sin(lnx) dx/x = Int sin t
dt

Int sin t dt = - cos t +
C

We'll replace t by ln x:

Int
sin(lnx) dx/x = - cos (ln x) + C

The
primitive function is: y = - cos (ln x) + C.