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Indefinite Integral (1)
 
Question: How do we do an indefinite integral such as
 
Yours Truly answers:
Listen to my audio feed as you read the answer below. 
 
As the first step, we should concentrate on the indefinite integral of  
sin(2x), without the  5. This is because the  5  is a constant multiple that “sticks around” throughout the computations.
 
(1) The moment we see  
sin(2x), think of  cos(2x)  whose derivative is  –2sin(2x).
 
(2) So, in order to end up with
 sin(2x)  when differentiated, we need to start instead with

(3) Since the  5  sticks around, we would have


 
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