If ∫$$11+x2$$−$$1(1+x)2xdx=$$−−

Correct option is 4tan−1x−x1+x32+C

Questions

$If \int \frac{1}{1 + x^{2}} - \frac{1}{(1 + x) 2 \sqrt{x}} d x = - -$

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cot−1x+x1−xx+C

sin−1x+C

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tan−1x−x1+x32+C

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detailed solution

Correct option is D

I=∫11+x2−1(1+x)2xdx=∫11+x2dx−∫11+(x)212xdx=∫11+x2dx−∫11+t2dt( where x=t)=tan−1⁡x−tan−1⁡x+C=tan−1⁡x−x1+x32+C

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If ∫11+x2−1(1+x)2xdx=−−

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$If \int \frac{1}{1 + x^{2}} - \frac{1}{(1 + x) 2 \sqrt{x}} d x = - -$