Question

What is `\int _ { 0} ^ { 1} \frac { x ^ { 3} + 1} { x + 1} d x`?

Answer 1

`int (x^3+1)/(x+1) dx = int ((x+1)(x^2-x+1))/(x+1 dx`

Explanation:

`= int (x^2-x+1) dx = x^3/3-x^2/2+x`

Now evaluate fro 0 to 1 to get `1/3-1/2+1 = 5/6`