Question Detail
Question
Obtain the integral ∫ (eˣ / (4 + eˣ)) dx.
Correct Answer
Option C is the correct answer.
Detailed Explanation
This integral can be solved using a simple u-substitution.Let u = 4 + eˣ.Then, the derivative of u with respect to x is du/dx = eˣ.So, du = eˣ dx.Substitute u and du into the integral:∫ (1 / u) du.This integrates to ln|u| + C.Substitute back u = 4 + eˣ:ln|4 + eˣ| + C.Since 4 + eˣ is always positive, we can write it as ln(4 + eˣ) + C.
Hint
Look for a function in the denominator whose derivative is in the numerator. A u-substitution is likely appropriate.