求∫√(1+r*r)dr 20
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∫ 1/[r(d - r)] dr
= (1/d)∫ [r + (d - r)]/[r(d - r)] dr
= (1/d)∫ [1/(d - r) + 1/r] dr
= (- 1/d)∫ d(d - r)/(d - r) + (1/d)∫ 1/r dr
= (- 1/d)ln|d - r| + (1/d)ln|r| + C
= (1/d)ln|r/(d - r)| + C
= (1/d)∫ [r + (d - r)]/[r(d - r)] dr
= (1/d)∫ [1/(d - r) + 1/r] dr
= (- 1/d)∫ d(d - r)/(d - r) + (1/d)∫ 1/r dr
= (- 1/d)ln|d - r| + (1/d)ln|r| + C
= (1/d)ln|r/(d - r)| + C
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是根号下（1+r*r)的定积分
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