∫(0,1) ln(x+1)² dx= 2∫(0,1) ln(x+1) dx= 2xln(x+1) - 2∫(0,1) x * 1/(x+1) dx= 2[(1)ln2] - 2∫(0,1) [(x+1)-1]/(x+1) dx= 2ln2 - 2∫(0,1) dx + 2∫(0,1) dx/(x+1)= 2ln2 - 2x + 2ln|x+1|= 2ln2 - 2 + 2l...