(a)[3]
Find the value of $\int \frac{4 + e^x}{2e^{2x}}\, dx$.
(b)[4]
Without using a calculator, find the value of $\int_2^{10} \frac{1}{2x + 5}\, dx$, and give the answer 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 and the lines $x = 0$, $x = 6$ and $y = 0$ is labelled $R$. Use the trapezium rule with $2$ strips to estimate the area of $R$, and give your answer correct to $1$ decimal place.