Find the general soloution of the ODE

I'm having a little trouble finding the general solution for this ordinary differential equation.

(cos y)dy/dx = x + x siny

In latex form it looks like this (copy the link into your browser)
http://latex.codecogs.com/gif.latex?(cos%20y)\frac{dy}{dx}=x%20+%20x%20sin%20y

All help is appreciated and a quick explanation of how you got to the solution would be brilliant.

Thanks

cos y dy/dx = x(1+sin y)

multiply both sides by dx/(1+sin y)

cos y /(1+sin y) dy = x dx

∫ cos y /(1+sin y) dy = ∫ x dx --------(1)

Let 1+sin y = u
cos y dy = du
∫ cos y /(1+sin y) dy = ∫ du/u = ln u = ln (1+sin y)

(1) becomes:

ln (1+sin y) = x^2/2 + C1
(1+sin y) = e^(x^2/2)+C1
1+ sin y = e^(x^2/2) e^C1
1+sin y = Ce^(x^2/2)
sin y = C e^(x^2/2) - 1

Its (cosy)dy/dx = x(1+siny)
or cosy/(1+siny) dy = xdx.
So integrating, ln(1+siny)= (x^2)/2 + c. Hope it suffices.