how to numerically integrate to machine precision?

I want to write a MATLAB code for \frac{\partial{gh}}{\partial\theta}=-\left(afu+u^{2}\tan{\theta}\right)

[SL: edited to add the equation in math format. If you click the sigma in the Insert section of your post's toolstrip, you can directly enter a LaTeX equation and have it formatted nicely.]

[Kayode Odeyemi]

OK. Thanks