Question

How do you integrate `f(x)=(sqrtx-1)(sqrtx+1)` using the product rule?

Answer 1

`1/2x^2-x+C`

Explanation:

Use identity `(a+b)(a-b)=a^2-b^2`

In our case `(sqrtx-1)(sqrtx+1)=x-1`

`int(x-1)dx=intxdx-intdx=1/2x^2-x+C`