S=積分符號
S x^3*e^(x^2) dx
微積分->[部份績分]
2011-05-05 1:59 am
回答 (4)
2011-05-06 1:44 am
參考: 專家
2011-05-06 4:56 am
考慮 [x^2e^(x^2)]'=2xe^(x^2)+2x^3e^(x^2)
x^3e^(x^2) dx
=(1/2)x^2e^(x^2)-∫xe^(x^2) dx
=(1/2)x^2e^(x^2)-(1/2)e^(x^2)+C
x^3e^(x^2) dx
=(1/2)x^2e^(x^2)-∫xe^(x^2) dx
=(1/2)x^2e^(x^2)-(1/2)e^(x^2)+C
2011-05-05 3:27 am
請問是使用部分積分嗎?!
2011-05-05 2:13 am
∫ x^3*e^(x^2) dx
Set y=x^2
dy=2xdx
∫ x^3*e^(x^2) dx
=(1/2)∫2 x*x^2*e^(x^2) dx
=(1/2)∫y*e^(y) dy
u=y，dv=e^ydy
∫ x^3*e^(x^2) dx
=(1/2)∫y*e^(y) dy
=(1/2)[y*e^y－∫e^ydy+c1]
=(1/2)[y*e^y－e^y+c1]
=(1/2)[x^2*e^(x^2)－e^(x^2)]+c
Set y=x^2
dy=2xdx
∫ x^3*e^(x^2) dx
=(1/2)∫2 x*x^2*e^(x^2) dx
=(1/2)∫y*e^(y) dy
u=y，dv=e^ydy
∫ x^3*e^(x^2) dx
=(1/2)∫y*e^(y) dy
=(1/2)[y*e^y－∫e^ydy+c1]
=(1/2)[y*e^y－e^y+c1]
=(1/2)[x^2*e^(x^2)－e^(x^2)]+c
收錄日期: 2021-04-30 15:55:22
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https://hk.answers.yahoo.com/question/index?qid=20110504000010KK05208