If $$I=$$∫$$1+x21$$−$$x2dx$$ then I is equal to

Question

If $$I=$$∫$$1+x21$$−$$x2dx$$ then I is equal to

Infinity Learn · Accepted Answer

$$I=$$∫$$1+x21$$−$$x2$$  $$1+x21+x2dx=$$∫$$1+x2dx1$$−$$x21+x2I=$$∫$$1dx1$$−$$x21+x2+$$∫$$x2dx1$$−$$x21+x2I=$$∫$$dx1$$−$$x21+x2$$−∫−$$x2dx1$$−$$x21+x2I=$$∫$$dx1$$−$$x21+x2$$−∫$$1$$−$$x2$$−$$1dx1$$−$$x21+x2I=$$∫$$11$$−$$x21+x2dx$$−∫$$1$$−$$x2dx1$$−$$x21+x2+$$∫$$1dx1$$−$$x21+x2I=2$$∫$$dx1$$−$$x21+x2$$−∫$$dx1+x2I=2$$∫$$dxx21x2$$−$$1x1+1x2$$−log⁡$$x+1+x2Put$$ $$1x2+1=t2$$ in $$1st$$  integral −$$2x3dx=dt2tdxx3=$$−$$tdt=I=2$$∫−$$tdtt2$$−$$2t$$−log⁡$$x+x2+1=I=2$$∫$$tdt(2)2$$−$$t2$$−log⁡$$x+x2+1+C=I=2$$⋅$$122log$$⁡$$2+t2$$−t−log⁡$$x+1+x2+C=I=12log$$⁡$$2+1x2+12$$−$$1x2+1$$−log⁡$$x+1+x2+C=I=12$$ $$log2x+1+x22x$$−$$1+x2$$ −$$logx+1+x2+C$$

$If I = \int \frac{\sqrt{1 + x^{2}}}{1 - x^{2}} d x then I is equal to$

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If I=∫1+x21−x2dx then I is equal to

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$If I = \int \frac{\sqrt{1 + x^{2}}}{1 - x^{2}} d x then I is equal to$