∫x^2lnxdx =∫lnxd(x³/3)=x³/3lnx-∫x³/3d(lnx)=x³/3lnx-∫x³/(3x)dx=x³/3lnx-∫x²/3dx=x³/3lnx-x³/9
∫e^(-2x)sin(x/2)dx=∫(-1/2)sin(x/2)d[e^(-2x)]=-1/2*e^(-2x)sin(x/2)-∫(-1/2)[e^(-2x)]d[sin(x/2)]
=-1/2*e^(-2x)sin(x/2)-∫(-1/4)[e^(-2x)]cos(x/2)dx
=-1/2*e^(-2x)sin(x/2)-∫(1/8)cos(x/2)d[e^(-2x)]
=-1/2*e^(-2x)sin(x/2)-{(1/8)cos(x/2)e^(-2x)-∫(1/8)[e^(-2x)]d(cos(x/2)}
=-1/2*e^(-2x)sin(x/2)-{(1/8)cos(x/2)e^(-2x)-∫(-1/16)[e^(-2x)](sin(x/2)dx}
∫e^(-2x)sin(x/2)dx=-(4*(cos(x/2)/2 + 2*sin(x/2)))/(17*exp(2*x))