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INTEGRATE
x2+1/ (x+1)2
Hi Abhishek,
MAke the sub x+1 = t.
So the integral will be {t^2 - 2t + 2}/t^2 = 1 - 2/t + 2/t^2
Which is directly integrable.
Best Regards,
Ashwin (IIT Madras).
integral of X2+1/(x+1)2
ans.. x-2log(x+1)-2/x+1 +C
ANS IS X-2[(1/X+1)+LN(X+1)]
∫{(x2+1)/(x+1)2}dx
=∫(x2+1+2x-2x)/(x2+1+2x)}dx
=∫{(x2+1+2x)/(x2+1+2x)}dx-∫{(2x+2-2)/(x2+1+2x)}dx
=∫1.dx-∫{(2x+2)/(x2+1+2x)}dx+∫{2/(x+1)2}dx
=x-∫(1/t)dt+2(-1)(x+1)-1 ...................................[Let x2+1+2x=t→(2x+2)dx=dt]
=x- ln ιtι - 2/(x+1) + c
=x- ln ιx2+1+2xι - 2/(x+1) + c...............where ιxι represents logarithm of x.
write x2+1 as (x+1)2-2x
integrate
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