If $$f(x)$$ is a polynomial satisfying $$f(x)$$⋅$$f1x=f(x)+f1x$$ and $$f(3)=82$$, then ∫$$f(x)x2+1dx=$$

Correct option is 3x33−x+2tan−1x+c

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$If f (x) is a polynomial satisfying f (x) \cdot f (\frac{1}{x}) = f (x) + f (\frac{1}{x}) and f (3) = 82, then \int \frac{f (x)}{x^{2} + 1} d x =$

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x3−x+2tan−1x+c

13x3−x+tan−1x+c

x33−x+2tan−1x+c

13x3+x+2tan−1x+c

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detailed solution

Correct option is C

Let f(x)=xn+1f(3)=82⇒3n+1=82⇒3n=34∴n=4∫x4+1x2+1dx=∫x2−1+2x2+1dx

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If f(x) is a polynomial satisfying f(x)⋅f1x=f(x)+f1x and f(3)=82, then ∫f(x)x2+1dx=

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Ready to Test Your Skills?

free study material

$If f (x) is a polynomial satisfying f (x) \cdot f (\frac{1}{x}) = f (x) + f (\frac{1}{x}) and f (3) = 82, then \int \frac{f (x)}{x^{2} + 1} d x =$