`int (1 - tan^2(x))/(sec^2(x)) dx` Evaluate the integral

`int(1-tan^2(x))/(sec^2(x))dx`

Rewrite the integrand as,

`int(1-tan^2(x))/(sec^2(x))dx=int(1-(sin^2(x))/(cos^2(x)))/(1/(cos^2(x)))dx`

`=int(cos^2(x)-sin^2(x))dx`

Now use the following identities:

`cos^2(x)=(1+cos(2x))/2`

`sin^2(x)=(1-cos(2x))/2`

`=int((1+cos(2x))/2-(1-cos(2x))/2)dx`

`=int(1+cos(2x)-1+cos(2x))/2dx`

`=intcos(2x)dx`

`=sin(2x)/2`

add a constant C to the solution,

`=sin(2x)/2+C`