∫2^x*3^x/(9^x-4^x) dx

∫2^x*3^x/(9^x-4^x) dx
= ∫(2/3)^xdx/[1-(4/9)^x]
= [ln(2/3)]^(-1)∫d[(2/3)^x]/{1-[(2/3)^x]^2}
= {[ln(2/3)]^(-1)∫d[(2/3)^x]/[1-(2/3)^x] + [ln(2/3)]^(-1)∫d[(2/3)^x]/[1+(2/3)^x]}/2
= [ln(2/3)]^(-1)[ln|(2/3)^x + 1| - ln|(2/3)^x - 1|]/2