Trigonometric integration

Trigonometric integration

1. (sin^nx)

   • n=even
     • ∫1/2-1/2 Cos2x dx
   • n=odd
     • ∫Sin^3xdx
       • ∫Sin^2x Sinx dx
         • ∫[1-Cos^2x] Sindx

2. (Cos^nx)

   • n=even
     • ∫1/2+1/2 Cos2x dx
   • n=odd
     • ∫Cos^3xdx
       • ∫Cos^2x Cosx dx
         • ∫[1-Sin^2x] Cosdx

3. (Sin^nx)(Cos^mx)

   • n and m even
     • ∫(1/2-1/2 Cos2x)(∫1/2-1/2 Cos2x dx) dx
       • ∫1/4-1/4 Cos^2(2x) dx
   • n =odd m=even
     • ∫Sin^3x Cos^2x dx
       • ∫Sinx Sin^2x Cos^2x dx
         • ∫Sinx(1-Cos^2x)Cos^2x dx
   • n=even m=odd
     • ∫Cos^3x Sin^2x dx
       • ∫Cosx Cos^2x Sin^2x dx
         • ∫Cosx(1-Sin^2x)Sin^2x dx