∫ 6/e^3x + 6e^2x + 11e^x + 6 dx ; x ∈ (0,∞)

Question

\(\int\limits_{0}^{∞}\frac{6}{e^{3x}+6e^{2x}+11e^x+6}dx\)

(1) \(log_{e}(\frac{512}{81})\)

(2) \(log_{e}(\frac{32}{27})\)

(3) \(log_{e}(\frac{256}{81})\)

(4) \(log_{e}(\frac{64}{27})\)

Answer 1

(2) \(log_{e}(\frac{32}{27})\)