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Find f(x) if f'(x)=11e^x/(11+e^x).
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We have to find the integral of f'(x)=11e^x/(11+e^x)
let 11 + e^x = y
e^x dx = dy
Int [ 11e^x/(11+e^x) dx]
=> Int [ 11dy/y]
=> 11*ln |y| + C
substitute y = 11 + e^x
=> 11*ln |(11 + e^x)| + C
For f'(x) = 11e^x/(11+e^x), f(x) = 11*ln |(11 + e^x)| + C
Posted by justaguide on April 15, 2011 at 2:15 AM (Answer #2)
Best answer as selected by question asker.
The function we have to find out is called primitive and it is noted as F(x). To determine F(x), we'll solve the indefinite integral using substitution technique:
11+e^x = t
We'll differentiate both sides:
e^xdx = dt
Int 11e^xdx/(11+e^x) = 11*Int dt/t
11*Int dt/t = 11*ln |t| + C
We'll replace t by 11+e^x and we'll apply power property of logarithms:
F(x) = Int 11e^xdx/(11+e^x) = ln [(11+e^x)^11] + C
Posted by giorgiana1976 on April 15, 2011 at 2:17 AM (Answer #3)
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