y＝∫ln(2＋t²)dt＝tln(2＋t²)-∫td(ln(2＋t²))＝tln(2＋t²)-∫t*2t/(2＋t²)dt＝tln(2＋t²)-∫2(t²＋2)/(2＋t²)-4/(2＋t²)dt＝tln(2＋t²)-2t＋∫(2√2)/(1＋(t/√2)²)d(t/√2)＝tln(2＋t²)-2t＋2√2arctan(t/√2)把(e∧x，0)代入得y＝(e∧x)ln(2＋e∧(2x))-2e∧x＋2√2arctan((e∧x)/√2)
则dy/dx＝
如图
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