to integrate e divide by the derivative of the power, leave the power the same..

the power is (-3x)Ln(x) which is differentiated using the product rule f'g+g'f

f=-3x f'=-3 g=ln(x) g'=1/x the differential of the power is -3ln(x)+-3x/x which simplifies to -3ln(x)-3

The integral of y= e^(-3x)Ln(x) is therfore y= (e^(-3x)Ln(x))/(-3ln(x)-3)+c