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INTEGRATE x 2 +1/ (x+1) 2

INTEGRATE



x2+1/ (x+1)2


Grade:12th pass

6 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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).

suraj kumar
5 Points
9 years ago

integral of   X2+1/(x+1)2

 ans..    x-2log(x+1)-2/x+1  +C

 

arjun ahluwalia
15 Points
9 years ago

ANS IS X-2[(1/X+1)+LN(X+1)]

Jaskaran Singh
15 Points
9 years ago

1354_47661_int.JPG

Menka Malguri
39 Points
9 years ago

∫{(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.

INTURI SUHAS REDDY
29 Points
9 years ago

write x2+1 as (x+1)2-2x

integrate

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