Make the substitution , so you end up with
; use by parts on the first term and , you will then end up with
Thus, , make all the re-subs and final should be...
Im solving an the integral of using trig substitution. I have it down to so I add the one integral over to the other side and get and then I get but my solutions manual has I'm just confused as to why I can't add the other integral over to get 10. It seems with other integration by parts problems you can but for some reason with the sec(x)^3 they don't add it over?