Answer :

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,


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