∫ sec 3 ( x ) tan ( x ) {\displaystyle \int \sec ^{3}(x)\tan(x)\,}
u = sec ( x ) {\displaystyle u=\sec(x)}
d u = sec ( x ) tan ( x ) d x {\displaystyle du=\sec(x)\tan(x)\,dx}
∫ sec 3 ( x ) tan ( x ) = ∫ u 2 d u {\displaystyle \int \sec ^{3}(x)\tan(x)\,=\int u^{2}\,du}
= 1 3 u 3 + c {\displaystyle ={\frac {1}{3}}u^{3}\,+\,c}
= 1 3 sec 3 ( x ) + c {\displaystyle ={\frac {1}{3}}\sec ^{3}(x)\,+\,c}
