You realize that is the derivative of .
here's some more u should know by heart
and so on we use like 30 maybe "basic" integrals, like table integrals which u can use without calculating them and with some basic operations, and substitutions (and a lot of practice) u can solve probably (for sure) any integral that u can get to do in your school
For your original question, you have been told that this integral is .
The way they get this result is through trigonometric substitution. Trigonometric substitutions are handy to know, because through the use of the trigonometric identities, you can usually simplify the problem...
Let so that . Note that this means .
Then
.