AP EAMCET · Maths · Definite Integration
\(\int_0^{\infty}\left(x^{12}+x^{-12}\right) \frac{\log x}{x} d x=\)
- A \(0\)
- B \(1\)
- C \(\log 2\)
- D \(e^2\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(I=\int_0^{\infty}\left(x^{12}+x^{-12}\right) \frac{\log x}{x} d x\) Put \(t=\frac{1}{x} \Rightarrow d t=-\frac{1}{x^2} d x\) \(\Rightarrow \quad-x d t=\frac{1}{x} d x \Rightarrow-\frac{d t}{t}=\frac{1}{x} d x\)…
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