integral of 2^x+4sinh(x)

解

\int 2^{x} + 4 sinh (x) d x

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

解答ステップ

\int 2^{x} + 4 sinh (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 sinh (x) d x

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

\int 4 sinh (x) d x = 4 cosh (x)

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

定数を解答に追加する

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