$$ \begin{flalign} &(a) \quad \text{Calculate: } \int_{0}^{1} \frac{x^3 - 1}{\ln x} \, \mathrm{d}x && \&(b) \quad \text{Solve the equation: } \sqrt{3x-1}+\sqrt[3]{2x-5}=3 \&(c) \quad \text{Let } f(x)=\frac{2x^3-3x^2-12x+5}{x^2+2x+1}. \\ &\text{Determine the asymptotes of the graph of the function } f(x). \&(d) \quad \text{Calculate: } \lim_{x\to\infty} \left(\frac{3x-1}{3x+2}\right)^{2x+1} \&(e) \quad \text{Calculate: } \sum_{k=1}^{n} \left(\frac{1}{k}-\frac{1}{k+2}\right) \&(f) \quad \text{Let } f(x)=\ln\left(\frac{2x-1}{x+2}\right). \\ &\text{Determine the domain of the function } f(x). \&(g) \quad \text{Solve the inequality: } \log_3(x-1) + \log_3(x-2) \leq 1 \&(h) \quad \text{Calculate: } \binom{10}{4} \&(i) \quad \text{Calculate: } \int \frac{\cos^2 x}{1+\sin x} \, \mathrm{d}x \&(j) \quad \text{Calculate: } \lim_{x\to 0} \frac{\sin^2 x}{x^2} && \\end{flalign} $$