Integration of  (tanx)/(secx + tanx) dx

multi. nd divide given function by-tanx + secx

u will gett tanx(secx-tanx)/sec²x- tan²x

now denomenator becoms 1

left part is to int. secx .tanx +tan²x

int secx .tanx +int tan²x

secx . +int sec²x-1

finaly

secx+tanx-x +c