设由方程$e^{xy}-xy^{2}=e^{2}$确定的函数为$y = y(x)$，求$\left.\dfrac{dy}{dx}\right|_{x = 0}$.

求定积分$\int_{0}^{\dfrac{\pi}{2}}2\sin^{2}x\cos xdx$.

计算不定积分$\int\dfrac{\sqrt{x}+2}{x + 3}dx$.