1.25: Logarithmic and trigonometric integration

Given that $\displaystyle\int_{1}^{a}\left(\frac{1}{x} - \frac{1}{2x + 3}\right)\mathrm{d}x = \ln 3$, where $a > 0$, find the exact value of $a$, giving your answer in simplest surd form.

Find the exact value of $\displaystyle\int_{0}^{\pi/3}\left(\sin\left(2x + \frac{\pi}{3}\right) - 1 + \cos 2x\right)\mathrm{d}x$.