Integral of (ln^6x)/x dx

Answer 1

Try substitution of u=lnx,
du = dx/x
dx=xdu

∫ln^6(x)dx/x
=∫ln^6(x)dx/x
=∫u^6*xdu/x
=∫u^6du
=u^7/7+C
=ln^7(x)/7 + C