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(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 dx/(3 + 5sin^2 x): even in both => divide by cos^2 x, substitute t = tan x
• integral dx/(2 + sin x): none of the above => Weierstrass