You should write your rearrangement as
and then integrate. I'm not sure I buy your integration. Try again.
(except that you had "y" instead of "dy")
Now integrate both sides: the integral of a constant is that constant times x and the integral of x is
is correct. The integral of isbut cannot see where this 2nd part comes from.
Perhaps you misread the as .
is different from the solution in the book. The solution in the book is
can you show me where im goin wrong please. many thanks