limx→0(∫上x下0ln(1+t)dt)∧2/x∧4

Question

lim x→0(∫上x下0ln(1+t)dt)∧2/x∧4

Answer 1

lim (x→0) (∫[0,x]ln(1+t)dt)^2/x^4
=lim(x→0) 2ln(1+x)∫[0,x]ln(1+t)dt/(4x^3)
=lim(x→0) 2x∫[0,x]ln(1+t)dt/(4x^3)
=lim(x→0) ∫[0,x]ln(1+t)dt/(2x^2) (0/0)
=lim(x→0) ln(1+x)/(4x)
=1/4