求定积分$\int_{4}^{9} \dfrac{\sqrt{x}}{\sqrt{x}-1}dx$.

求$y = e^x-\dfrac{e}{2}x^2$的凹凸区间与拐点.

求由直线$x = 0$，$x = 2$，$y = 0$和曲线$y = e^x$所围成的图形绕$x$轴旋转一周所形成的旋转体的体积.