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How to determine the function f(x) if f'(x)=2e^ln(2x+3)/(2x+3)?
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To determine the primitive function f(x), we must calculate the indefinite integral of f'(x).
We'll apply substitution technique, replacing ln(2x+3) by t.
ln(2x+3) = t
We'll differentiate both sides and we'll get:
2dx/(2x+3) = dt
We'll re-write the integral in the new variable:
Int 2e^(ln(2x+3)) dx/(2x+3) = Int e^t*dt
Int e^t*dt = e^t + C
Int 2e^(ln(2x+3)) dx/(2x+3) = e^(ln(2x+3)) + C
The requested primitive function is: f(x) = e^(ln(2x+3)) + C
Posted by giorgiana1976 on May 19, 2011 at 2:19 PM (Answer #1)
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