TITLE: Indefinite integral of $\frac{\tan{(1+x^2)}}{1+x^2}$
QUESTION [7 upvotes]: Let $f(x) = \frac{\tan{(1+x^2)}}{1+x^2}$ , find $\int f(x)dx$ . I've tried many substitutions (including trigonometric substitutions like $x=\tan \theta$ ) and also integration by parts but didn't work . We can apply power series but it doesn't solve problem .

REPLY [2 votes]: Use Mittag-Leffler Expansion of tangent,
$\int\dfrac{\tan{(1+x^2)}}{1+x^2}~dx=\int\sum\limits_{n=0}^\infty\dfrac{8}{(2n+1)^2\pi^2-4(x^2+1)^2}~dx$