\int \operatorname { sec } x ( \operatorname { sec } x + \operatorname

1.	\int \operatorname { sec } x ( \operatorname { sec } x + \operatorname { tan } x ) d x
Answer» Multiply secx in bracket =int. sec^2x+secx.tanx =tanx+c+ int. sinx dx /cos^2 Take cosx=t Then after differentiating- >-sinxdx=dt put it in above equation =tanx + int. 1 dt/t^2 =tanx+c+(-1/t)+b =tanx-1/cosx + C (Where b,c C are constant)

\int \operatorname { sec } x ( \operatorname { sec } x + \operatorname { tan } x ) d x

Answer»

Multiply secx in bracket

=int. sec^2x+secx.tanx

=tanx+c+ int. sinx dx /cos^2

Take cosx=t

Then after differentiating-

>-sinxdx=dt put it in above equation

=tanx + int. 1 dt/t^2

=tanx+c+(-1/t)+b

=tanx-1/cosx + C

(Where b,c C are constant)