怎么算含有未知常量的定积分?x/(x+k)^2x从0到r

Question

怎么算含有未知常量的定积分? x/(x+k)^2 x从0到r

Answer 1

∫x/(x+k)^2dx
=∫(x+k-k)/(x+k)^2dx
=∫1/(x+k)dx-k∫1/(x+k)^2dx
=ln|x+k|+k/(x+k)+C