Problem : sin(2x)dx
 cos(2x) + c 

Note here that we need to multiply the initial result for the antiderivative by a correction
factor of
. To see why this is the case, take the derivative of the result to see
how to get back to the original function (remember to use the chain rule!).
Problem : cos(3x + 4)dx
sin(3x + 4) + c 

Again, a correction factor, this time equal to
, is needed.