Definite Integration

Let \(f\) be a twice differentiable function on \(\mathbb{R}\). If \(f^{\prime}(0)=4\) and \(f(x) + \int\limits_0^x {(x - t)f'(t)dt = \left( {{e^{2x}} + {e^{ - 2x}}} \right)\cos 2x + {2 \over a}x}\), then \((2 a+1)^{5}\, a^{2}\) is equal to _______________.