[tex]\int\limits {(tgx+tg^3x)} \, dx = \int\limits{tgx}dx+ \int\limits {tg^3x} \, dx[/tex]
[tex]\int{tg^nx}dx = \frac{tg^{n-1}}{n-1}-\int tg^{-2+n}xdx[/tex]
[tex]\int{tg^3x}dx = \frac{tg^{2}x}{2}-\int tgxdx[/tex]
[tex]\int\limits {(tgx+tg^3x)} \, dx = \int\limits{tgx}dx+ \frac{tg^{2}x}{2}-\int tgxdx[/tex] = [tex]\frac{1}{2} tg^2x+C[/tex]
