The integration by parts formula: S:udv/dx = uv - S:v*du/dx, where S: means "Integral of with respect to x"
Let 2*x be u and sin(x) be dv/dx
So du/dx =2 and v= -cos(x)
(3x+1)/x +(2x-1)/3 = (2x2 + 8x + 3)/3x by cross multiplying.
So equation becomes 2x2+ 8x + 3 = -9x by multiplying both sides by 3x. Adding 9x to both sides gives 2x2