∫a^2x dx =

1)a^x lna + C

2)a^2x/(2lnx) + C

3)a^2x lna + C

4)a^2x/(2lna) + C

Let's solve the given integral ∫a^2x dx:

We can use the formula for integrating exponential functions, which states that ∫a^u du = (a^u) / ln(a) + C, where C is the constant of integration.

So, in this case, we have a = a^2 and u = x. Substituting these values into the formula, we get:

∫a^2x dx = (a^2x) / ln(a^2) + C

Since ln(a^2) = 2ln(a), we can simplify this expression further:

∫a^2x dx = (a^2x) / (2ln(a)) + C

Therefore, the correct answer is:

2)a^2x/(2ln(a)) + C