A useful rule to remember....
Let be an antiderivative of .
Then, ( ),
Meaning whenever you have a linear function (of the form ax+b) you just take the coefficient with the "x" (the slope of line) and invert it.
For example,
Since this is a linear expression inside,
.
You can use the rule I told you.
Just find the anti-derivative the regular way,
But of course this answer is wrong, you need to invert the slope.
Thus,
Now let us find,
Note is a linear function in the special form we had above because is just a number in front.
Thus, to find the integral you just find the integral of sine which is -cosine and then invert the slope.
Thus,
.
Learn, this rule, it saves much time.