integrate (1+x 2 )/(1-2x 2 cosα + x 4 ) α belongs to (0,∏) w.r.t x

integrate (1+x2)/(1-2x2cosα + x4) α belongs to (0,∏) w.r.t x

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Suchita,


Please note, this is a standard integration which is integrated as follows.


Divide Nr and Dr by x2, and then write the denominator as,

(x-1/x)2 + 2 - 2cos2α.

Now make the substitution x-1/x = t, so that

1+1/x2 dx = dt

And the integral is of the form 1/(t2 + a2) dt ------ where a2 = 2-2cos2α.

And this is an integral, which is integrated by the standard formula of tan-1(x/a).


Hope that helps.


All the best,


Ashwin (IIT Madras).

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