MHT CET · Maths · Definite Integration
\(\int_1^3 \frac{\log x^2}{\log \left(16 x^2-8 x^3+x^4\right)} \mathrm{d} x=\ldots\)
- A 1
- B 3
- C \(\log 2\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(I = \int_1^3 \frac{2 \log x}{2 \log (x(4-x))} \mathrm{d} x = \int_1^3 \frac{\log x}{\log (x(4-x))} \mathrm{d} x\) \(2I = \int_1^3 \frac{\log x}{\log (x(4-x))} \mathrm{d} x + \int_1^3 \frac{\log (4-x)}{\log ((4-x)(4-(4-x)))} \mathrm{d} x\)
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