Solution of an indefinite integral of the form ∫ln(αx)lnln(αx)/xdx by the method of integration by parts, where α takes the values 1,2,3,4,5,…n.
An example of solving integrals for α=1, α=2, α=3 is considered.

∫ln(αx)lnln(αx)/xdx, ∫ln(x)lnln(x)/xdx, ∫ln(2x)lnln(2x)/xdx, ∫ln(3x)lnln(3x)/xdx

The solution is in PDF format