I got this problem from John.E.Freund's Mathematical_Statistics_with_Applications.
the question is,
If X has the probability density $$f(x)= \begin{cases} e^x& x>0\\ 0& \text{elsewhere} \end{cases}$$find the expected value of $g(X) = e^{3X/4}$.
In chapter 4 it shows that the expectation is $\int_{0}^{\infty}e^{3x/4}e^{-x}dx$,
I have no idea why it's $$e^{3x/4}e^{-x}$$ here, shouldn't it be $$e^{3x/4}e^{x}? $$
I checked the 7th and 8th editions of the book, and both show the first version, I think there must be something missed in my mind.Could you please help me to solve the question? Thanks very much. ：）