3.60: Differentiate a quotient and integrate tan

0606/11/O/N/25 — Question 7 · 7 marks

(a)
Differentiate sinxex+3cosx1\dfrac{\sin x}{\mathrm{e}^{x}} + 3\cos x - 1 with respect to xx.
[4]
(b)
Find (1+3tan2x)dx\displaystyle\int (1 + 3\tan^{2} x)\,\mathrm{d}x.
[3]