Verified answer

∫Cos√x.dx =[Cambio x=t² --> dx=2t·dt]=

∫2t·Cost.dt =[Partes: u=2t --> du=2·dt // dv=cost·dt --> v=sent]=

2t·sent - ∫ 2·sent dt =

2t·sent +2·cost + C =[deshago el cambio --> t=√x] =

2·√x·sen√x +2· cos√x + C

saludos