(a)[3]
Calculate $\int \frac{4 + e^x}{2e^{2x}}\, dx$.
(b)[4]
Without a calculator, Calculate $\int_{2}^{10} \frac{1}{2x + 5}\, dx$, and give the result in the form $\ln k$.
(c)[3]
The diagram shows the curve $y = \log_{10}(x + 2)$ for $0 \leq x \leq 6$. The region enclosed by the curve together with the lines $x = 0$, $x = 6$ and $y = 0$ is labelled $R$. Use the trapezium rule with 2 strips to estimate the area of $R$, giving your answer correct to 1 decimal place.