Hello, confusedgirl!
Watch very carefully . . .
We have: .
Then: .
. . For the second integral, use "normal" substitution.
. . We have: .
. . Let: .
. . Substitute: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Although we have completed the integration, your book's answer
. . is often simplified beyond all recognition.
Here's how they do it . . .
We have: .
Factor: . . . . . hope you followed that!
. . . .
. . . . . . . . ta-DAA!