Re: [積分] 兩題分部積分
※ 引述《mosb (摩斯漢堡)》之銘言：
: 1.
: ∫x(lnx)^2 dx
2
= (x^2 / 2 ) * (lnx) - ∫ xlnx dx
2
= (x^2 / 2 ) * (lnx) - (x^2 / 2 ) * lnx + ∫ x / 2 dx
2
= (x^2 / 2 ) * (lnx) - (x^2 / 2 ) * lnx + x^2 / 4 + C
: 2.
: ln2
: ∫ o xe^xdx
: 我算出來是
: =(x-1)e^x 怎麼帶值進去我不會
: 不知道怎麼會變成2ln2-1
: 請強者為我解惑謝謝^^
x ln2
= (x-1) * e |
0
ln2 0
= (ln2 - 1 ) * e - (0-1) * e
= 2 * ( ln2 - 1 ) + 1
= 2ln2 - 1
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