CBSE Class 12-science Answered
Evaluate:
∫((x^2+1))/((x^4+1) ) dx
Asked by Manoj | 09 Mar, 2013, 07:32: AM
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 +2] as x2+1/x2 = (x-1/x)2 +2
Let (x-1/x)=t so dt=(1+1/x2 )dx
Therefore, the integral becomes
I = dt/(t2 +2)
1/(2)1/2 tan-1t/(2)1/2 +c
Now, substitute value of t in above to get the answer.
Answered by | 10 Mar, 2013, 03:54: PM
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