Notice it's the product of 1/stuff and 1/(1+ the square of that stuff)
(and 1/(1 + a square) is a standard integrand)
Just in case a picture helps...
... where
... is the chain rule, and you're looking for F. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).
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