JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\int \limits_0^{\infty} \frac{6}{e^{3 x}+6 e^{2 x}+11 e^x+6} d x\)
- A \(\log _e\left(\frac{512}{81}\right)\)
- B \(\log _e\left(\frac{32}{27}\right)\)
- C \(\log _e\left(\frac{256}{81}\right)\)
- D \(\log _e\left(\frac{64}{27}\right)\)
Answer & Solution
Correct Answer
(B) \(\log _e\left(\frac{32}{27}\right)\)
Step-by-step Solution
Detailed explanation
\(1=\int \limits_0^{\infty} \frac{6}{\left(e^x+1\right)\left(e^{ x }+2\right)\left( e ^{ x }+3\right)} dx\) \(=6 \int \limits_0^{\infty}\left(\frac{\frac{1}{2}}{ e ^{ x }+1}+\frac{-1}{ e ^{ x }+2}+\frac{\frac{1}{2}}{ e ^{ x }+3}\right) d x\)…
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