Question

integrala din tg x*tg^3 x dx

Answer 1

$\int\limits {(tgx+tg^3x)} \, dx = \int\limits{tgx}dx+ \int\limits {tg^3x} \, dx$

$\int{tg^nx}dx = \frac{tg^{n-1}}{n-1}-\int tg^{-2+n}xdx$

$\int{tg^3x}dx = \frac{tg^{2}x}{2}-\int tgxdx$

$\int\limits {(tgx+tg^3x)} \, dx = \int\limits{tgx}dx+ \frac{tg^{2}x}{2}-\int tgxdx$ = $\frac{1}{2} tg^2x+C$