Evaluate \displaystyle \int_1^{10} \left(\sqrt{x} + 1\right)^3 dx - \int_1^{10} \left(\sqrt{x} - 1\right)^3 dx .

Answer 1

Hint:

For x > 0, you have

(sqrt(x) + 1)^3 - (sqrt(x) - 1)^3 =

6 x + 2