Question 3

Consider the following integral:

$$\int_0^1 \frac{(3t - 1) \hspace{3pt}dt}{(t + 1)(t + 5)}.$$

• Determine the expansion of the integrand $${\frac{3t - 1}{(t + 1)(t + 5) }}$$ in terms of partial fractions.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• Hence evaluate the integral.