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括号内变形后无穷近似值代换，
=e^(xln(1+1/x))(e^((x+1)ln(1+1/(x+1))-xln(1+1/x))-1)
~e((x+1)ln(1+1/(x+1))-xln(1+1/x))
lim=lime((x+1)ln(1+1/(x+1))-xln(1+1/x))/(1/x²)
=lime(ln(1+1/(x+1))-1/(x+2)-ln(1+1/x)+1/(x+1))/(-2/x³)
=lime(-1/(x+1)(x+2)+1/(x+2)²+1/x(x+1)-1/(x+1)²)/(6/x^4)
=limex^4(-1/(x+1)(x+2)²+1/x(x+1)²)
=limex^4((x+2)²-x(x+1))/x(x+1)²(x+2)²
=limex³(3x+4)/(x+1)²(x+2)²
=3e
=e^(xln(1+1/x))(e^((x+1)ln(1+1/(x+1))-xln(1+1/x))-1)
~e((x+1)ln(1+1/(x+1))-xln(1+1/x))
lim=lime((x+1)ln(1+1/(x+1))-xln(1+1/x))/(1/x²)
=lime(ln(1+1/(x+1))-1/(x+2)-ln(1+1/x)+1/(x+1))/(-2/x³)
=lime(-1/(x+1)(x+2)+1/(x+2)²+1/x(x+1)-1/(x+1)²)/(6/x^4)
=limex^4(-1/(x+1)(x+2)²+1/x(x+1)²)
=limex^4((x+2)²-x(x+1))/x(x+1)²(x+2)²
=limex³(3x+4)/(x+1)²(x+2)²
=3e
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