The sharing solution is as follows. Let t=arctanx. ∴x=tant。 Original formula = ∫ cost ln (tante) dt = sintln (tante)-∫ section dt.

∫sectdt=ln 丨 sect+tante+C. ∴ Original formula = sintln (tante)-ln 丨 sect+tante+C.

∴ Original formula =(xlnx)/√( 1+x? ) -ln 丨 x+√( 1+x? ) 丨+C.

For reference.