$$ \begin{flalign} &(a) \quad \int \frac{\cos x}{\sin^3 x} dx &&\\ &(b) \quad \lim_{x\to 0} \frac{\ln(1 + x^2) - \sin x}{x^4} \\ &(c) \quad \frac{d}{dx}\left[\int_0^{\sqrt{x}} \frac{\cos t^2}{\sqrt{1 + t^2}} dt\right] \\ &(d) \quad \int_0^1 \frac{\ln(1 - x)\ln(1 + x)}{x} dx \\ &(e) \quad \lim_{n\to\infty} \sum_{k=1}^n \frac{1}{(n + k)^2} \\ &(f) \quad \frac{d^2y}{dx^2} + 2\frac{dy}{dx} + 2y = \cos x \\ &(g) \quad \int_0^{\pi/2} \frac{\cos^2 x}{1 + \sin^2 x} dx \\ &(h) \quad \lim_{x\to 0} \left(\frac{1 - \cos x}{\sin x}\right)^{\cot x} \\ &(i) \quad \frac{d}{dx}\left[\int_{x^2}^{e^x} \frac{\ln t}{t} dt\right] \\ &(j) \quad \int \frac{1}{(x+1)(x^2+1)} dx && \end{flalign} $$