Factor #10# outside of the integral; this can be done as #10# is just a constant. Doing this cleans up the work a little, although it doesn't change the final answer.
#10intdx/x#
Recall that #intdx/x=ln|x|+C#.
First, note that we have the absolute value sign around #x# because #ln(x)# doesn't exist if #x# is negative. We want to avoid that. Furthermore, note that the natural log function is appropriate, because differentiating #ln(x)# gives us back #1/x,# the function we were originally trying to integrate. Finally, don't forget the constant of integration, #C#, as we must account for any possible constants (there are infinitely many -- the derivative of a constant is always #0#, #C# could be any value).
#10intdx/x=10ln|x|+C#