1 Answer | Add Yours
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
We’ve answered 396,217 questions. We can answer yours, too.Ask a question