integral of 2^{tan(x)}sec^2(x)

解

\int 2^{t a n (x)} sec^{2} (x) d x

\frac{2 ^{t a n (x)}}{ln ( 2 )} + C

解答ステップ

\int 2^{t a n (x)} sec^{2} (x) d x

u置換積分法を適用する

= \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{2 ^{u}}{ln ( 2 )}

代用を戻す

u = tan (x)

= \frac{2 ^{t a n (x)}}{ln ( 2 )}

定数を解答に追加する

= \frac{2 ^{t a n (x)}}{ln ( 2 )} + C