Calculate ∫ (tan(x))^2 dx.

To calculate the integral of ((\tan(x))^2), we can use a fundamental identity from trigonometry:

[

\tan^2(x) = \sec^2(x) - 1.

]

By substituting this identity into the integral, we have:

[

\int \tan^2(x) , dx = \int (\sec^2(x) - 1) , dx.

]

This can be split into two separate integrals:

[

\int \tan^2(x) , dx = \int \sec^2(x) , dx - \int 1 , dx.

]

The integral of (\sec^2(x)) is a well-known result:

[

\int \sec^2(x) , dx = \tan(x).

]

On the other hand, the integral of (1) with respect to (x) is simply:

[

\int 1 , dx = x.

]

Combining these results gives:

[

\int \tan^2(x) , dx = \tan(x) - x + C,

]

where (C) is the constant