Question

How do you integrate `int (2t^2-1)^2dt`?

Answer 1

`(4t^5)/5 -(4t^3)/3 +t +C`

Explanation:

Expand `(2t^2-1)^2 = 4t^4 - 4t^2 +1`

Now integrate term by term,

`int (4t^4-4t^2+1)dt = (4t^5)/5 -(4t^3)/3 +t +C`