Question Detail
Question
Obtain ∫(2/(2-3x))dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
This integral can be solved using a u-substitution. Let u = 2-3x.Then, differentiate u with respect to x: du/dx = -3, which implies du = -3dx, or dx = -du/3.Substitute u and dx into the integral:∫(2/u) (-du/3) = (-2/3) ∫(1/u) du.The integral of 1/u is ln|u|. So, we have:(-2/3)ln|u| + C.Substitute back u = 2-3x:(-2/3)ln|2-3x| + C.Option D matches this result.
Hint
Use a u-substitution with u = 2-3x. Remember that ∫(1/u) du = ln|u| + C.