Evaluate ∫₀^π dx/(5 + 3 cos x).

Evaluate ∫₀^π dx/(5 + 3 cos x).

• A. π/4
• B. π/2
• C. π/8
• D. π

Answer: A) π/4

Explanation: Using substitution tan(x/2) = t, cos x = (1−t²)/(1+t²), dx = 2 dt/(1+t²). Limits: 0 to π → t from 0 to ∞. Integral becomes ∫₀^∞ [2/(1+t²)] / [5 + 3(1−t²)/(1+t²)] dt = ∫₀^∞ 2 dt / (5(1+t²)+3−3t²) = ∫₀^∞ 2 dt/(8+2t²) = ∫₀^∞ dt/(4+t²) = [ (1/2) tan⁻¹(t/2) ]₀^∞ = (1/2)(π/2 − 0) = π/4.