1)u=x²⇒du=2xdx;dv=sin2xdx⇒v=-1/2*cos2x
Sx²sin2xdx=1/2*x²cos2x+Sxcos2xdx=
u=x⇒du=dx;dv=cos2xdx⇒v=1/2*sin2x
=1/2*x²cos2c+1/2*xsin2x-1/2Ssin2xdx=
=1/2*x²cos2x+1/2*xsin2x+1/4cos2x+C
2)S(4x+1)dx/x(x-1)²=S(1/x-1/(x-1)+5/(x-1)²)dx=lnx-ln(x-1)-5/(x-1)+C
3)S(2x²+x+4)dx/(x+1)(x²+4)=S(x/(x²-4)+1/(x+1)dx=
u=x²+4⇒du=2xdx
=1/2Sdu/u+Sdx/(x+1)=1/2lu+ln(x+1)=1/2*ln(x²+4)+ln(x+1)+C
4)S(x²-1)dx/√(x-2)=
u=√(x-2)⇒du=dx/2√(x-2)
=2S[(u²+2)²-1]du=2S(u^4+4u²+4)du-2Sdu=2/5*u^5+8/3*u³+8u-2u=
=2/5*√(x-2)^5+8/3*√(x-2)³+6√(x-2)+C