JEE Mains · Maths · STD 12 - 7.1 indefinite integral
The integral \(\int \frac{ e ^{3 \log _{e} 2 x }+5 e ^{2 \log _{ e } 2 x }}{ e ^{4 \log _{e} x }+5 e ^{3 \log _{e} x }-7 e ^{2 \log _{e} x }} dx , x > 0\), is equal to ....... . (where \(c\) is a constant of integration)
- A \(\log _{ e }\left| x ^{2}+5 x -7\right|+ c\)
- B \(4 \log _{ e }\left| x ^{2}+5 x -7\right|+ c\)
- C \(\frac{1}{4} \log _{ e }\left| x ^{2}+5 x -7\right|+ c\)
- D \(\log _{ e } \sqrt{ x ^{2}+5 x -7}+ c\)
Answer & Solution
Correct Answer
(B) \(4 \log _{ e }\left| x ^{2}+5 x -7\right|+ c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{ e ^{3 \log _{ e } 2 x }+5 e ^{2 \log _{ e } 2 x }}{ e ^{4 \log _{ e } x }+5 e ^{3 \log _{ e } x }-7 e ^{2 \log _{ e } x }} dx , x > 0\)…
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