what is the integral of e^(2 ln u) du ?

Answer 1

This is a tricky problem, but it has an easy solution.

Note that 2 ln u = ln u^2. That means:

e^(2 ln u) = e^(ln u^2) = u^2.

What this problem is really wanting you to do is integrate u^2 du.

The integral of u^2 du is:

(u^3)/3 + c.

Answer 2

e^(2 ln u) = e( ln u²) = u².
Integrating u² gives u³/3 + C

Answer 3

exp(2*ln(u)) = u^2, so the integral is u^3/3.