Partial fractions

Examples

1. 1)

   $$\int \frac{dt}{t^2+6t+8}$$

2. 2)

   $\star$

   $$\int \frac{t}{t^2+6t+8}𝑑t$$

3. 3)

   $$\int \frac{3t+1}{{(t+3)}^2}𝑑t$$

   (There are two ways to do this.)

4. 4)

   $\star$

   $$\int \frac{3t+1}{{(t+3)}^2(t+1)}𝑑t$$

5. 5)

   $$\int \frac{t^3-3t+1}{t^2+6t+10}𝑑t$$