The value ∫$$dxx4+5x2+4$$ IS

Correct option is 4(1/3)tan−1⁡x−(1/6)tan−1⁡(x/2)+C

Questions

The value $\int \frac{d x}{x^{4} + 5 x^{2} + 4}$ IS

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(1/3)tan−1⁡x−(1/2)tan−1⁡(x/2)+C

3tan−1⁡(x/3)+2tan−1⁡(x/2)+C

(1/3)tan−1⁡x+(1/6)tan−1⁡(x/2)+C

(1/3)tan−1⁡x−(1/6)tan−1⁡(x/2)+C

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detailed solution

Correct option is D

I=∫dxx4+5x2+4=∫dxx2+1x2+4=∫131x2+1−1x2+4dxTherefore, I=13tan−1⁡x−16tan−1⁡x2+C.

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The value ∫dxx4+5x2+4 IS

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The value $\int \frac{d x}{x^{4} + 5 x^{2} + 4}$ IS