Find a function of the $\displaystyle f(x) = \lambda e^{2x} + \mu e^{x} - \nu x$ where $\displaystyle \lambda, \mu, \nu$ are independent of $\displaystyle x$ and $\displaystyle f(0) = -1$, $\displaystyle f'(\log_{e} 2) = 30$ and $\displaystyle \int_{0}^{\log_{e} 4} \{f(x) + \nu x\} dx = 28.5$