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,