Define an integral function

In terms of evaluate the following:

- .
- .
- .
- .

- First, we make the substitution so . The bounds of integration are then
Therefore we have,

- For this one, make the substitution , . The bounds of integration don’t change since and . So we have,
- To compute this in terms of , we integrate by parts. Let
Therefore we have

- We use integration by parts again, this time let
Therefore we have,