Question

Question #25019

Answer 1

(i) `a^3+b^3=(a+b)(a^2-ab+b^2), and so, x^3+1=x^3+1^3=(x+1(x^2-x+1)`. (ii) `5/6`

Explanation:

(ii) `int((x^3+1)/(x+1) dx = int(x+1)(x^2-x+1)/(x+1) dx=int(x^2-x+1) dx=[x^3/3-x^2/2+x]`, between the limits 0 and 1
Answer; `[1/3-1/2+1]=5/6`.