With a good knowledge of derivatives and integration formulas and with some practice you will develop an "eye" for substitutions which can be made to make an integral easy to solve. In this case I see whose derivative is which is present in your integrand! And since sin is an easy integral to solve the problem becomes very easy.
First we'll manipulate the integrand Algebraically:
Now we start our substitution.
Let
Then
and, in differential form:
We can substitute these into
giving:
which integrates to:
Substituting back in for v we get:
(