Finding two functions of an indefinite integral

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MooreLikeMike

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The question I'm working on ask to " Find ∫(e^(3x-1)e^(2x+2)-3/(4x+1)) dx. Find two functions g (x) and h (x) such that g' (x) = (e^(3x-1)e^(2x+2)-3/(4x+1)) = h' (x)

I found the antiderivative for the first function:1/5*e^(5x+1)-3/4*ln(abs(4x+1))+C. I just don't know how I'm supposed to find two functions from this. I thought that maybe I could write this function down twice, but change the constant "C" for both functions so that technically it would be two different functions. But I don't think that's right. I know that the function that I found can satisfy g (x) OR h (x), but not both without them being identical.
 

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MooreLikeMike said:
The question I'm working on ask to " Find ∫(e^(3x-1)e^(2x+2)-3/(4x+1)) dx. Find two functions g (x) and h (x) such that g' (x) = (e^(3x-1)e^(2x+2)-3/(4x+1)) = h' (x)

I found the antiderivative for the first function:1/5*e^(5x+1)-3/4*ln(abs(4x+1))+C. I just don't know how I'm supposed to find two functions from this. I thought that maybe I could write this function down twice, but change the constant "C" for both functions so that technically it would be two different functions. But I don't think that's right. I know that the function that I found can satisfy g (x) OR h (x), but not both without them being identical.
Click to expand...
You say your problem statement is:

" Find ∫(e^(3x-1)e^(2x+2)-3/(4x+1)) dx. Find two functions g (x) and h (x) such that g' (x) = (e^(3x-1)e^(2x+2)-3/(4x+1)) = h' (x)

Is that your EXACT problem statement?

Because "as posted" - it does not make sense!
 
If one anti-derivative of f is F then F+ 8 and F+ 30 are two different functions with derivative f. More generally, F+ c, where c is any constant, has derivative f.
 
Subhotosh Khan said:
You say your problem statement is:

" Find ∫(e^(3x-1)e^(2x+2)-3/(4x+1)) dx. Find two functions g (x) and h (x) such that g' (x) = (e^(3x-1)e^(2x+2)-3/(4x+1)) = h' (x)

Is that your EXACT problem statement?

Because "as posted" - it does not make sense!
Click to expand...
Yes, this is EXACTLY how the question is posed. That make sense as to why I was confused then
 
HallsofIvy said:
If one anti-derivative of f is F then F+ 8 and F+ 30 are two different functions with derivative f. More generally, F+ c, where c is any constant, has derivative f.
Click to expand...
Then I was correct in thinking that changing the constant would be the way to complete the question?
 
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