If $$I=$$∫$$2$$−$$x2(1+x)1$$−$$x2dx$$ then I is equal to

Question

If $$I=$$∫$$2$$−$$x2(1+x)1$$−$$x2dx$$ then I is  equal to

Infinity Learn · Accepted Answer

Let $$I=$$∫$$2$$−$$x2(1+x)1$$−$$x2dxI=$$∫$$1$$−$$x2+1(1+x)1$$−$$x2dxI=$$∫$$1$$−$$x2(1+x)1$$−$$x2dx+$$∫$$dx(1+x)1$$−$$x2I=$$∫$$(1$$−$$x)dx1$$−$$x2dx+$$∫$$dx(1+x)1$$−$$x2I=$$∫$$11$$−$$x2dx+$$∫$$($$−$$x)dx1$$−$$x2+$$∫$$dx(1+x)1$$−$$x2I=$$$$sin$$−$$1$$⁡$$x+1$$−$$x2+I1$$ Where $$I1=$$∫$$1(1+x)1$$−$$x2dx$$ Put $$1+x=1t$$⇒$$x=1t$$−$$1$$⇒$$dx=$$−$$1t2dtI1=$$∫−$$1t2dt1t1$$−$$1t$$−$$12=$$∫−$$1dtt2$$−$$1$$−$$2t+t2I1=$$∫−$$12t$$−$$1dt=$$−$$1222t$$−$$1+CI1=$$−$$21+x$$−$$1+C=$$−$$1$$−$$x1+x+C$$∴$$I=$$$$sin$$−$$1$$⁡$$x+1$$−$$x2$$−$$1$$−$$x1+x+C$$

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

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If I=∫2−x2(1+x)1−x2dx then I is equal to

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