To evaluate the definite integral 2∫1 (e^1/x3)/x^4 dx, we can use the following formula:
∫f(x)dx = F(b) - F(a),
where F(x) is the antiderivative of f(x).
The antiderivative of (e^1/x3)/x^4 is F(x) = -e1/x3/x3 + c.
Therefore, our answer is F(1) - F(2):
2∫1 (e^1/x3)/x^4 dx = -e1/13/13 + c - (-e1/23/23 + c) = e1/23/23.