Evaluate: ∫ [dx / (e^x + e^(-x))].

Answer and explanation

Correct answer: B. tan^(-1)(e^x) + C

  1. Step 1: Multiply numerator and denominator by e^x: ∫ [e^x dx / (e^(2x) + 1)].
  2. Step 2: Let u = e^x, du = e^x dx.
  3. Step 3: ∫ [du / (u^2 + 1)] = tan^(-1)(u) + C = tan^(-1)(e^x) + C.

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