Determine indefinite integrals of the form ∫ 𝑓(𝑎𝑥 + 𝑏)𝑑𝑥.

Determine \(\int (3x + 5)^4 \, dx\).

Determine ∫(3x - 2)⁴ dx

A pharmaceutical company models the rate of change of drug concentration in the bloodstream using derivatives. The table below shows four different rate functions and their corresponding drug codes. Determine the drug concentration function \( C(t) \) for Drug B and Drug D, where \( t \) is time in hours and \( C \) is measured in micrograms per millilitre (μg/mL). Express your answers in simplified form with the constant of integration. (a) Determine \( C(t) \) for Drug B. (2 marks) (b) Determine \( C(t) \) for Drug D. (3 marks)

Determine the following indefinite integrals. (a) \(\int (2x + 3)^4 \, dx\) (1 mark) (b) \(\int 5e^{3x - 1} \, dx\) (1 mark) (c) \(\int \frac{2}{4x + 5} \, dx\) (1 mark)