The indefinite integral is ln(x)+c. A definite integral would be [ln(x)] in the interval [a,b], which evaluates to ln(b)-ln(a)=ln(b/a)={1 0 1/e e}. These are all the options. That is, b/a={e 1 e^(1/e) e^e} and b={ae a ae^(1/e) ae^e}. Of all these the most likely answer is ae. So, if we put a=1, b=e, and the integral is ∫(1/x)dx between the limits 1 and e=ln(e/1)=ln(e)=1 answer a. Another possible interval [a,b] is a=e, b=e² or any interval where a and b are e to any power n such that b=eⁿ⁺¹ and a=eⁿ, including negative integer values for n. For example, n=-1 makes a=1/e or e⁻¹, and b=1, i.e., [1/e,1]. Also, if p is any number, a=peⁿ, b=peⁿ⁺¹ works to give a definite integral which evaluates to 1, for example, a=πe², b=πe³.