Correct option is 3−13tan−1x+23tan−1x2+c

Questions

$\int \frac{x^{2}}{(x^{2} + 1) (x^{2} + 4)} d x =$

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13tan−1x−23tan−1x2+c

−13tan−1x−23tan−1x2+c

−13tan−1x+23tan−1x2+c

13tan−1x+23tan−1x+c

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detailed solution

Correct option is C

Let x2=y Split in to partial fractions ∫134x2+4-1x2+1dx =23tan-1x2-13tan-1x+c

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∫x2x2+1x2+4dx=

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$\int \frac{x^{2}}{(x^{2} + 1) (x^{2} + 4)} d x =$