[tex]\int f(x)g_{0}(x)dx = f(x)g_1x-f'(x)g_2(x) f''(x)g_3(x)-...[/tex]
[tex]g_{i 1}(x)=\int g_i(x)dx[/tex]

[tex]sin a * cos b = \frac{1}{2}\left [ sin(a b) sin(a-b) \right ][/tex]
[tex]cos a * cos b = \frac{1}{2}\left [ cos(a b) cos(a-b) \right ][/tex]
[tex]sina * sinb = \frac{1}{2}\left [ cos(a b)-cos(a-b) \right ][/tex]

[tex]cos^2x=\frac{1 cos2x}{2}[/tex]
[tex]sin^2x=\frac{1-cos2x}{2}[/tex]

[tex]sinx*cosx=\frac{1}{2}sin2x[/tex]