let-W-x-arctan-xt-2-2-t-2-dt-1-find-a-explicit-form-of-f-x-2-find-the-value-of-t-2-2-t-2-1-x-2-t-4-dt-

Question Number 48063 by maxmathsup by imad last updated on 18/Nov/18

l e t W (x) = \int_{- \infty}^{+ \infty} \frac{a r c t a n ({x t}^{2})}{2 + t^{2}} d t

1) f i n d a e x p l i c i t f o r m o f f (x)

2) f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{t^{2}}{(2 + t^{2}) (1 + x^{2} t^{4})} d t .