Evaluate the integral of tan^4(x) dx.

The integral of tan^4(x) dx is (1/3)tan^3(x) - tan(x) + x + C.

To evaluate the integral of tan^4(x) dx, we can use the trigonometric identity tan^2(x) = sec^2(x) - 1. We can rewrite the integral as:

∫tan^4(x) dx = ∫tan^2(x) * tan^2(x) dx
= ∫(sec^2(x) - 1) * tan^2(x) dx

Let u = tan(x), then du/dx = sec^2(x) and dx = du/sec^2(x). Substituting these into the integral, we get:

∫(sec^2(x) - 1) * tan^2(x) dx = ∫(u^2 - 1) du
= (1/3)u^3 - u + C
= (1/3)tan^3(x) - tan(x) + C

Therefore, the integral of tan^4(x) dx is (1/3)tan^3(x) - tan(x) + x + C.