Re: [積分] 我想問兩題INTEGRATION BY PARTS

[youyouyou (第3年高3生活)]

※ 引述《tomho1202 (never regreat)》之銘言：
:        x(e)^2x             1     e^2x
: ∫————————dx  =   ---  -------  +c
:        (2x+1)^2            4    (2x+1)
           2x              2x
   d      e             4xe
 ---   ----------  =  ---------
  dx     2x+1          (2x+1)^2

: ∫ x(x-1)^1/2 dx
       2
 =∫ (u  +1 ) u *2udu
     4    2
=∫2u + 2u du  = (2/5)(x-1)^(5/2) + (2/3)(x-1)^(3/2) + c

let  u= (x-1)^(1/2)

   2udu =dx



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推 GBRS:第二題也可將x(x-1)^(1/2)改成[(x-1)+1](x-1)^(1/2)