Definite Integration

Let \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) be defined as \(f(x)=a e^{2 x}+b e^x+c x\). If \(f(0)=-1, f^{\prime}\left(\log _e 2\right)=21\) and \(\int_0^{\log _e 4}(f(x)-c x) d x=\frac{39}{2}\), then the value of \(|a+b+c|\) equals