integral of 1/(sinX +secX) dx
multiply numerator and denominator by sec2x
let tanx =t
=> sec2x dx =dt
and solve the eq.in the form of 't '.
convery in sin and cos form-
then rationalise. it will be ((cosx/(1-sin^2x cos^2x) - (cos^2x sinx/(1-cos^2x sin^2x))
then put sinx=t in one part and cosx = t in other. solve as usual..
some mistake in ur suggestion,
when you multiply & divide sec2 x u will get it as sec2 x/(tan xsec x+sec3 x) dx.
but, exact answer is too long and still many of them didn 't solve.!!!!!!