integral of (2^x-4sin(x))

解

\int (2^{x} - 4 sin (x)) d x

\frac{2 ^{x}}{ln ( 2 )} + 4 cos (x) + C

解答ステップ

\int 2^{x} - 4 sin (x) d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2^{x} d x - \int 4 sin (x) d x

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

\int 4 sin (x) d x = - 4 cos (x)

= \frac{2 ^{x}}{ln ( 2 )} - (- 4 cos (x))

簡素化

= \frac{2 ^{x}}{ln ( 2 )} + 4 cos (x)

定数を解答に追加する

= \frac{2 ^{x}}{ln ( 2 )} + 4 cos (x) + C