Evaluate the integral: integral of (1 / (2x + 1)) dx.
Answer and explanation
Correct answer: B. (1/2) ln|2x + 1| + C
- Step 1: Let u = 2x + 1, then du = 2 dx, so dx = du / 2.
- Step 2: The integral becomes (1/2) * integral of (1/u) du = (1/2) ln|u| + C = (1/2) ln|2x + 1| + C.
Answer
(1/2) ln|2x + 1| + C.
Why not the others: 'ln|2x + 1| + C' forgets to divide by the inner derivative 2; '2 ln|2x + 1| + C' multiplies by 2 instead of dividing; '-(1/2) / (2x + 1)^2 + C' applies power rule erroneously to a logarithmic form.
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