AP EAMCET · Maths · Definite Integration
\(\int_0^1 \frac{2 x+5}{x^2+3 x+2} \mathrm{~d} x=\)
- A \(\log \left(\frac{16}{3}\right)\)
- B \(0\)
- C \(\log \left(\frac{3}{16}\right)\)
- D \(4 \log 2-2 \log 3\)
Answer & Solution
Correct Answer
(A) \(\log \left(\frac{16}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\int_0^1 \frac{2 x+5}{(x+1)(x+2)} \mathrm{~d} x=\int_0^1 \left(\frac{3}{x+1} - \frac{1}{x+2}\right) \mathrm{~d} x\) \(= [3 \log|x+1| - \log|x+2|]_0^1\) \(= (3 \log 2 - \log 3) - (3 \log 1 - \log 2)\) \(= 3 \log 2 - \log 3 - (0 - \log 2)\) \(= 4 \log 2 - \log 3\)…
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