ln ((x(x^2+1)^2)/(√(2x^3-1))

Answer 1

using your log rules
ln ((x(x^2+1)^2)/(√(2x^3-1))
= lnx + ln(x^2 + 1)^2 - ln(√(2x^3-1))
= lnx + 2ln(x^2 + 1) - (1/2)ln(2x^3 - 1)