AP EAMCET · Maths · Indefinite Integration
If \(\int \log \left(6 \sin ^2 x+17 \sin x+12\right)^{\cos x} d x=f(x)+c\) then, \(f\left(\frac{\pi}{2}\right)=\)
- A \(\frac{1}{6}\left[\log 5^5+\log 7^7-12\right]\)
- B \(\frac{1}{6}[7 \log 5+5 \log 7+29]\)
- C \(\frac{1}{6}[14 \log 5+15 \log 7+12]\)
- D \(\frac{1}{6}[15 \log 5+14 \log 7-29]\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{6}[15 \log 5+14 \log 7-29]\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \log \left(6 \sin ^2 x+17 \sin x+12\right)^{\cos x} d x\) Let \(\sin x=t \Rightarrow \cos x d x=d t\)…
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