`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`
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