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

`inttan^2(x)sec(x)dx`

use the identity:`tan^2(x)=sec^2(x)-1`

`inttan^2(x)sec(x)dx=int(sec^2(x)-1)sec(x)dx`

`=int(sec^3(x)-sec(x))dx` 

Now apply the Integral Reduction:`intsec^n(x)dx=(sec^(n-1)(x)sin(x))/(n-1)+(n-2)/(n-1)intsec^(n-2)(x)dx`

`intsec^3(x)dx=(sec^2(x)sin(x))/2+1/2intsec(x)dx` 

Use the common integral:`intsec(x)dx=ln(tan(x)+sec(x))`

`:.inttan^2(x)sec(x)dx=(sec^2(x)sin(x))/2+1/2intsec(x)dx-intsec(x)dx`

`=(sec^2(x)sin(x))/2-1/2intsec(x)dx`

`=(sec^2(x)sin(x))/2-1/2ln(tan(x)+sec(x))`

add a constant C to the solution,

`=(sec^2(x)sin(x))/2-1/2ln(tan(x)+sec(x))+C`