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#### righteous818

##### New member

- Jul 30, 2012

- 4

i am have been at this whole day can you tell me how to integrate 1/(x^2 +1)^2

- Thread starter righteous818
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- Thread starter
- #1

- Jul 30, 2012

- 4

i am have been at this whole day can you tell me how to integrate 1/(x^2 +1)^2

- Jan 26, 2012

- 890

integral 1/(x^2+1)^2 - Wolfram|Alphai am have been at this whole day can you tell me how to integrate 1/(x^2 +1)^2

and click on show steps.

CB

- Jan 29, 2012

- 661

An alternative: the problem is just routine if you know thei am have been at this whole day can you tell me how to integrate 1/(x^2 +1)^2

Denoting $q(x)=(x^2+1)^2$ we have

$q_1(x)=\gcd \left\{ q(x),q'(x)\right\}=\gcd \left\{ (x^2+1)^2,2x(x^2+1) \right\}=x^2+1$

$q_2(x)=\dfrac{q(x)}{q_1(x)}=x^2+1$

Then,

$\displaystyle\int \dfrac{1}{(x^2+1)^2}\;dx=\dfrac{Ax+B}{q_1(x)}+\int \dfrac{Cx+D}{q_2(x)}\;dx$

equivalently:

$\displaystyle\int \dfrac{1}{(x^2+1)^2}\;dx=\dfrac{Ax+B}{x^2+1}+\int \dfrac{Cx+D}{x^2+1}\;dx$

and we can determine $A,B,C,D$ differentiating both sides with respect to x.