Integrating secx(sex+tanx) and the steps !
i'm not sure which technique is supposed to be used here.. ex; integration by parts or substitution etc. !

Simply distrbution and direct application of memorized integrals

I will refer the integration sign as int

J = Int secx(secx + tanx ) dx = int sec^2x + secxtanx dx

Remember int sec^2x dx= tanx +c
Int secxtanx = secx +c

If you wanna their proof just request

J = tanx + secx +c

Where is the diagram