integral of (7cosh(x)+1+tan^2(x))

解

\int (7 cosh (x) + 1 + tan^{2} (x)) d x

7 sinh (x) + tan (x) + C

解答ステップ

\int 7 cosh (x) + 1 + tan^{2} (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 7 cosh (x) d x + \int 1 d x + \int tan^{2} (x) d x

\int 7 cosh (x) d x = 7 sinh (x)

\int 1 d x = x

\int tan^{2} (x) d x = - x + tan (x)

= 7 sinh (x) + x - x + tan (x)

簡素化

= 7 sinh (x) + tan (x)

定数を解答に追加する

= 7 sinh (x) + tan (x) + C