Some of those look ugly, but I can certainly help with the last one.

(I'm just going to put INT for integration)

INT ( x sin (2x) ) dx

You can integrate this by parts.

So let u = x and v'= sin 2x

then u' = 1 and v = 0.5 cos 2x

Then INT ( u v' ) dx = uv - INT ( v u' )

=> INT ( x sin (2x) ) dx = 0.5 x cos(2x) - 0.5 INT ( cos (2x) ) dx

= 0.5 x cos(2x) + 0.25 sin 2x + C