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,