∫1/(x^2+9)dx上限3下限0

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∫1/(x^2+9)dx上限3下限0∫1/(x^2+9)dx上限3下限0∫1/(x^2+9)dx上限3下限0用换元积分法,取x=3t,则原式化为:∫1/(x^2+9)dx=(1/3)×∫1/(t^2+

∫1/(x^2+9)dx上限3下限0
∫1/(x^2+9)dx上限3下限0

∫1/(x^2+9)dx上限3下限0
用换元积分法,取x=3t,则原式化为:
∫1/(x^2+9)dx=(1/3)×∫1/(t^2+1)dt(上限1,下限0)
=(1/3)(arctan1-arctan0)=派/12