Question

∫㏑（1+x）／（2-x）²dx 求积分,

Answer 1

原式=∫ln(1+x)/(x-2)² d(x-2)

=-∫ln(1+x)d[1/(x-2)]

=-ln(1+x)*1/(x-2)+∫1/(x-2) dln(1+x)

=-ln(1+x)*1/(x-2)+∫dx/(x-2)(x+1)

=-ln(1+x)*1/(x-2)+1/3*∫[1/(x-2)-1/(x+1)]dx

=-ln(1+x)*1/(x-2)+1/3*(ln|(x-2}-ln|x+1|)+C