Question

Решите интеграл
tg^2 (x)+1

Answer 1

$intlimits {(tg^2 (x)+1) } , dx =intlimits {( frac{sin^2(x)}{cos^2(x)}+1) } , dx =intlimits {( frac{sin^2(x)}{cos^2(x)}+frac{cos^2(x)}{cos^2(x)}) } , dx = \ \ =intlimits {frac{sin^2(x)+cos^2(x)}{cos^2(x)}} , dx =intlimits {frac{1}{cos^2(x)}} , dx =tg(x)+C$