Question

ln(1+x)的积分怎么算啊?

Answer 1

∫ln(1+x)dx = ∫ln(1+x)d(1+x) = ∫lntdt = tlnt - ∫td(lnt)
= tlnt - ∫dt = tlnt - t + C = (1+x)ln(1+x) - x + C