AP EAMCET · Maths · Indefinite Integration
Let \(f(x)=\int \frac{x}{\left(x^2+1\right)\left(x^2+3\right)} d x\). If \(f(3)=\frac{1}{4} \log \left(\frac{5}{6}\right)\) then \(f(0)=\)
- A \(\frac{1}{4} \log \left(\frac{1}{3}\right)\)
- B 0
- C \(\frac{1}{2} \log \left(\frac{1}{3}\right)\)
- D \(\log \left(\frac{1}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{4} \log \left(\frac{1}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\because f(x)=\int \frac{x}{\left(x^2+1\right)\left(x^2+3\right)} d x\) Let \(x^2=t \Rightarrow 2 x d x=d t\)…
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