vtckw412

題目首先要我搵 d/dx [x•e^(ax)] where a is a non-zero constant然後題目再要我in，Hence, or otherwise, 搵 $ [x•e^(ax)] dx
我只係讀M1，所以想問呢條in數，唔用integration by parts，有可能做到嗎？
求救！

pstrike

根本無人要求你識integration by parts...
實際上你只要in番你剛才d左ge result再調位就okay

(你識其實都無影響, 因為 integration by parts根本就係anti-d)

Calvin4

呢條數係用左by part既concept, 但係唔識by part都可以做到
let y=xe^ax
dy/dx=axe^(ax)+e^(ax)
積xe^(ax)dx
=1/a積axe^(ax)dx
=1/a積axe^(ax)+e^(ax)-e^(ax)dx
=1/a積axe^(ax)+e^(ax)dx-1/a積e^(ax)dx
=...

數痴夢王

let y=xe^ax
dy/dx=axe^(ax)+e^(ax)
   積xe^(ax)dx
=1/a積(dy/dx -e^(ax) dx
=y/a-1/a^2 e^(ax)+C where C is a constant.
=1/a*xe^(ax)-1/a^2 e^(ax)+C where C is a constant.