(0,1)表示积åçä¸éåä¸é
åå¼=â«(0,1) ln(1+x^2)dx
=x ln(1+x^2)â(0,1)-â«(0,1) xdln(1+x^2) åé¨ç§¯å
=ln2-â«(0,1) x*2x/(1+x^2)dx
=ln2-â«(0,1) [2-2/(1+x^2)]dx åå¼å为æ´æ°ä¸çåå¼ç代æ°å
=ln2-(2x-arctanx)â(0,1)
=ln2-2+Ï/4
åå¼=â«(0,1) ln(1+x^2)dx
=x ln(1+x^2)â(0,1)-â«(0,1) xdln(1+x^2) åé¨ç§¯å
=ln2-â«(0,1) x*2x/(1+x^2)dx
=ln2-â«(0,1) [2-2/(1+x^2)]dx åå¼å为æ´æ°ä¸çåå¼ç代æ°å
=ln2-(2x-arctanx)â(0,1)
=ln2-2+Ï/4
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