General form: integral R(sin x, cos x) dx

Method selection:

1. If R(-sin x, cos x) = -R(sin x, cos x) [odd in sin]: substitute t = cos x
2. If R(sin x, -cos x) = -R(sin x, cos x) [odd in cos]: substitute t = sin x
3. If R(-sin x, -cos x) = R(sin x, cos x) [even in both]: substitute t = tan x
4. If none of the above: use Weierstrass substitution t = tan$\frac{x}{2}$

Examples:

• integral $sin^3$ x * $cos^2$ x dx: odd in sin => t = cos x
• integral $sin^2$ x * $cos^3$ x dx: odd in cos => t = sin x
• integral $\frac{dx}{3 + 5sin^2 x}$: even in both => divide by $cos^2$ x, substitute t = tan x
• integral $\frac{dx}{2 + sin x}$: none of the above => Weierstrass