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Evaluate: ∫((x^2+1))/((x^4+1) ) dx

Asked by Manoj 9th March 2013, 7:32 AM
Answered by Expert
Answer:
I denotes for the value of integral.
 

(x2+1)/(x4+1)

Divide numerator and denominator by x2, we get:

(1+1/x2)/(1/x2+x2)

(1+1/x2)/[(x-1/x)+2]    as x2+1/x2 = (x-1/x)+2

Let (x-1/x)=t so dt=(1+1/x)dx

Therefore, the integral becomes

I = dt/(t+2)

1/(2)1/2  tan-1t/(2)1/2 +c   

Now, substitute value of t in above to get the answer.
Answered by Expert 10th March 2013, 3:54 PM
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