integrate by parts ln(x)/x^3

The question states to use integration by parts. So first we recall the integration by parts formula is integrate(u(x)v'(x)  dx)=     (v(x)u(x))    -    integrate(u'(x)v(x)   dx)+c (note these integrals are with respect to x.. u(x) v(x) are functions of x and u'(x)=du/dx). To integrate ln(x)/x^3 notice that ln(x)/x^3 can be written as ln(x)*1/x^3. Then we let u(x)=ln(x) as we can differentiate ln(x) to 1/x but cannot easily integrate ln(x). So v(x)=1/x^3 Putting this into the formula we get integrate(ln(x)/x^3  dx)=  -0.5x^(-2) *ln(x)-integrate(-0.5x^(-2)*x^(-1)  dx)+c=  -0.5ln(x)/x^2+1/(4x^2)+c