Q: solve diff equation:
[2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0
IF your ODE $\displaystyle M dx + N dy = 0$ is not exact ie. $\displaystyle M_y = N_x$ then one looks for an integrating factor $\displaystyle \mu $ such that
$\displaystyle \left(\mu M\right)_y = \left( \mu N \right)_x$
If $\displaystyle \mu = \mu(x)$ only then
$\displaystyle \frac{\mu_x}{\mu} = \frac{M_y-N_x}{N}$ which in your case it is (very fortunate)!