Evaluate the following integrals:

Let

We know a³ + b³ = (a + b)(a² – ab + b²)

Hence, in the numerator, we can write

x³ + 8 = x³ + 2³

⇒ x³ + 8 = (x + 2)(x² – x × 2 + 2²)

⇒ x³ + 8 = (x + 2)(x² – 2x + 4)

Therefore, we can write the integral as

Recall and

Thus,