AP EAMCET · Maths · Indefinite Integration
\(\int \frac{3 x+4}{x^3-2 x+4} d x=\log f(x)+C \Rightarrow f(3)=\)
- A \(\frac{1}{\sqrt{17}}\)
- B \(\frac{1}{17}\)
- C \(\frac{2}{15}\)
- D \(\frac{2}{17}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{17}}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{3 x+4}{x^3-2 x+4} d x=\log f(x)+C\) \(I=\int \frac{3 x+4}{x^3-2 x+4}\) Since, \(x^3-2 x-4=(x-2)\left(x^2+2 x+2\right)\) \(\frac{3 x+4}{x^3-2 x+4}=\frac{A}{(x-2)}+\frac{B x+C}{\left(x^2+2 x+2\right)}\) \(\Rightarrow 3 x+4=A\left(x^2+2 x+2\right)+(B x+C)(x-2)\) On…
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