In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Use the substitution $$\(u=\mathrm{e}^{x}-3\)$$ to show that where $$\(a\)$$ and $$\(b\)$$ are constants to be found. (7) (ii) Show, by integration, that $$\[ \int 3 \mathrm{e}^{x} \cos 2 x \mathrm{~d} x=p \mathrm{e}^{x} \sin 2 x+q \mathrm{e}^{x} \cos 2 x+c \]$$ where $$\(p\)$$ and $$\(q\)$$ are constants to be found and $$\(c\)$$ is an arbitrary constant. (5)

Answer:

Knowledge points:

Solution: