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

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,

Regards,

Ashwin (IIT Madras).

Approved