Show that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Solve the equation.

, µ

So first,

and

. Thus,

and

So this is inexact.

Then multiplying everything by µ we get

and

. Thus,

and

. So now they are exact

I have chosen to integrate N first since it's a bit easier than M. So integrating N I get

Then I differentiated this with respect to x getting

Then I compared this to M.

. So from this I get

and then

making my final answer

.

But according to my book the final answer is only

. I'm not sure where the

is going. Help please