Question

calcule as integrais indefinidas pelo metedo da substituição

∫ tg³ x × sec²x×dx

Answer 1

$\\</p><p>\int_{}^{}tg^2(x)tg(x)sec^2(x)dx\\</p><p>\\</p><p>\int_{}^{}(-1+sec^2(x))tg(x)sec^2(x)dx\\</p><p>\\</p><p>u=sec(x)\;du=sec(x)tg(x)dx\\</p><p>\\</p><p>\int_{}^{}(-1+u^2)udu\\</p><p>\\</p><p>\int_{}^{}(-u+u^3)du\\</p><p>\\</p><p>\frac{-u^2}{2}+\frac{u^4}{4}+C</p><p>\\</p><p>Voltando \;a\; subst.:</p><p>\frac{-sec^2(x)}{2}+\frac{sec^4(x)}{4}+C$