定积分(0到x)(t^2)/(1-t^2)dt -x+1/2*ln【(1+x)/(1-x)】我最主要是【(1+x)/(1-x)】算不出来,知道的麻烦这步写详细些,
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![定积分(0到x)(t^2)/(1-t^2)dt -x+1/2*ln【(1+x)/(1-x)】我最主要是【(1+x)/(1-x)】算不出来,知道的麻烦这步写详细些,](/uploads/image/z/1785368-56-8.jpg?t=%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%880%E5%88%B0x%EF%BC%89%28t%5E2%29%2F%281-t%5E2%29dt+-x%2B1%2F2%2Aln%E3%80%90%281%2Bx%29%2F%281-x%29%E3%80%91%E6%88%91%E6%9C%80%E4%B8%BB%E8%A6%81%E6%98%AF%E3%80%90%281%2Bx%29%2F%281-x%29%E3%80%91%E7%AE%97%E4%B8%8D%E5%87%BA%E6%9D%A5%EF%BC%8C%E7%9F%A5%E9%81%93%E7%9A%84%E9%BA%BB%E7%83%A6%E8%BF%99%E6%AD%A5%E5%86%99%E8%AF%A6%E7%BB%86%E4%BA%9B%EF%BC%8C)
定积分(0到x)(t^2)/(1-t^2)dt -x+1/2*ln【(1+x)/(1-x)】我最主要是【(1+x)/(1-x)】算不出来,知道的麻烦这步写详细些,
定积分(0到x)(t^2)/(1-t^2)dt
-x+1/2*ln【(1+x)/(1-x)】
我最主要是【(1+x)/(1-x)】算不出来,知道的麻烦这步写详细些,
定积分(0到x)(t^2)/(1-t^2)dt -x+1/2*ln【(1+x)/(1-x)】我最主要是【(1+x)/(1-x)】算不出来,知道的麻烦这步写详细些,
答案如图.
这个题主要是会分解,先把)(t^2)/(1-t^2)分解成t^-1+1/1-t^2,然后再把分母分解成(1-T)(1+T),应该会做了吧
(t^2)/(1-t^2)=-1+1/(1-t^2)=1+1/2(1-t)+1/2(1+t)
∫(0,x)t²/(1-t²)dt=∫(0,x)(t²-1+1)/(1-t²)dt=∫(0,x)1/(1-t²)+∫(0,x)1dt
=(1/2)∫(0,x)[1/(1+t)+1/(1-t)]dt+t=(1/2)∫(0,x)[1/(1+t)]dt+(1/2)∫(0,x)[1/(1-t)]dt+...
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∫(0,x)t²/(1-t²)dt=∫(0,x)(t²-1+1)/(1-t²)dt=∫(0,x)1/(1-t²)+∫(0,x)1dt
=(1/2)∫(0,x)[1/(1+t)+1/(1-t)]dt+t=(1/2)∫(0,x)[1/(1+t)]dt+(1/2)∫(0,x)[1/(1-t)]dt+t
={(1/2)[ln(1+t)-ln(1-t)]+t}(0,x)={(1/2)ln[(1+t)/(1-t)]+t}(0,x)
=(1/2)ln[(1+x)/(1-x)]-x
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