Question Detail
Question
Integrate ∫ex / √(1-ex) dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To integrate ∫ex / √(1-ex) dx, use u-substitution.Let u = 1 - ex.Then, the differential du = -ex dx, which means ex dx = -du.Substitute these into the integral:∫1/√u * (-du) = -∫u-1/2 duIntegrate u-1/2:- [u(-1/2)+1 / ((-1/2)+1)] + C= - [u1/2 / (1/2)] + C= -2√u + CSubstitute back u = 1 - ex:= -2√(1 - ex) + CThis matches option D.
Hint
Let u be the expression under the square root, 1 - ex. Then find du and substitute.