what is the integration for xln(x+1) dx?
回答 (2)
2011-10-25 2:14 pm
✔ 最佳答案
∫ x*ln(x+1) dx==½∫ ln(x+1) d(x²)=
=½x²ln(x+1) - ½∫ x² d(ln(x+1))=
=½x²ln(x+1) - ½∫ x²/(x+1) dx=
=½x²ln(x+1) - ½∫ (x²-1+1)/(x+1) dx=
=½x²ln(x+1) - ½∫ (x-1)(x+1)/(x+1)+1/(x+1) dx=
=½x²ln(x+1) - ½∫ x-1+1/(x+1) dx=
=½x²ln(x+1) - ¼ x² + x/2 -½ln(x+1) +C
http://www.wolframalpha.com/input/?i=%28%C2%BDx%C2%B2ln%28x%2B1%29+-+%C2%BC+x%C2%B2+%2B+x%2F2+-%C2%BDln|x%2B1|%29`
參考: ,
2011-10-25 8:57 pm
收錄日期: 2021-05-01 00:58:59
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https://hk.answers.yahoo.com/question/index?qid=20111025055415AA9JUXm