How Does Substituting t=e^x Simplify the Integral Calculation?

[eclayj]

Homework Statement

Mathematica's calculation of ∫₀^Log(2)Sin[($\pi$/2)e^2x]e^xdx = -FresnelS[1] + FresnelS[2]

Remembering that FresnelS[x] = ∫₀^tSin[($\pi$/2)t²]dt, You announce that a transformation you can use to help explain Mathematica's output is that every time x goes up by one unit, t=?


Not even sure how to approach this at all. Any suggestions or help on how to start this is appreciated!

 

[Char. Limit]

I'd start with a quick substitution, t=e^x. That'll make things real easy.