下列不定積分怎麼算?(抱歉,我不知道積分的符號怎麼打,所以寫得有點簡略)?

2016-03-17 5:00 am
1.x/(xlnx)
2.x/[x(lnx)^5]
3.x^2[(2x+3)^(1/3)]

回答 (1)

2016-03-18 3:46 am
✔ 最佳答案
1.
∫ x/(xlnx) dx
=∫1/(lnx) dx
=In|In x|+C

2.
∫ x/[x(lnx)^5] dx
=∫ 1/[(lnx)^5] dx
=∫ (In x)^-5 dx
=-025(In x)^-4 +C

3.
I=∫ x^2[(2x+3)^(1/3)] dx
設u=2x+3
x=(u-3)/2
du=2dx
du/2=dx
I=0.5∫ [(u-3)/2]^2[u^(1/3)] du
I=0.5(0.25)∫ (u^2 -6u+3)[u^(1/3)] du
I=0.125∫ (u^7/3 -6u^4/3 +3u^1/3)du
I=0.125[0.3u^10/3 -(18/7)(u^7/3) +(9/4)u^(2/3)]+C
I=0.375(2x+3)^(10/3) -(9/28)(2x+3)^(7/3) +0.28125(2x+3)^(2/3)+C


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原文連結 [永久失效]:
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